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Syllabus

if(-4,3)and(4,3)are two vertices of an equilateral triangle. find the coordinates of the third vertex. given that the origin lies in the interior of the triangle.

Find the ratio in which the line segment joining the points (-6 , 10) and(3 , -8 ) is divided by ( -4 , 6).How to prove three points collinear by Section Formula

Q1=Two opposite vertices of a square are (-1,2)and (3,2).Find the coordinates of other two vertices.Q2=If two opposite vertices of a square of a square are (5,4)and (1,-6) ,find the coordinates of its remaining two vertices.find the ratio in which the join of the points (1,2) and (-2,3) is divided by the line 3x + 4y = 7

THE VERTICES OF TRIANGLE ABC ARE A(4,6) , B(1,5) , C(7,2). A LINE IS DRAWN TO INTERSECT SIDES AB AND AC AT D AND E RESPECTIVELY SUCH THAT AD/AB=AE/AC=1/4. CALCULATE THE AREA OF TRIANGLE ADE AND COMPARE IT WITH AREA OF TRANGLE ABC.

if p(x,y ) is any point on the line segment joining the points A(a , 0) and B(0,b) then show that x/a + y/b = 1

xam idea model paper - 1 (unsolved-1)

Find the coordinates of the point which divides the line segment joining the points A(4, 3) and B(9, 7) in the ratio 3 : 2.

If the points A (1,-2) B (2,3)C (-3,2) D (-4,-3) are the vretices of parallelogram ABCD, then taking AB as the base find the height of the parallelogram

Determine the ratio in which the line 2x+y-4=0 divides the line segment joining point A(2,-2) & B(3,7)?

The area ( in square units) of the triangle formed by the points A( a,0) O(0,0) B(0,b) is ?

Find the centre of a circle passing through the points (6,-6), (3,7) and (3,3).

Find the coordinates of a point whose distance from (3,5) is 5 units and that from (0,1) is 10 units..

Find the value of 'p' for which the points (-1,3) , (2,p) and (5,-1) are collinear.

If A (4,-8) , B (-9,7) and C(18 , 13) are the vertices of triangle ABC, find the lenght of the median through A and coordinate of centroid of triangle.

Find the ratio in which the line 3x + y - 9 = 0 divides the line segment joining the points A(1,3) and B(2,7)

the mid points of the sides of a triangle are (3,4) , (4,1) , (2,0).find the coordinates of the vertices of the triangle.

if the point p (2,1) lies on the line segment joining point a (4,2) & B (8,4), then

IF P and Q are two points whose coordinates are ( at

^{2,},2at) and ( a/t^{2}, - 2a/t) respectively and S is the point ( a,0).. Show that 1/SP + 1/SQ is independent of tif three points (0,0) (3,root 3) and (3,k) form an equilateral triangle then k=?

In what ratio the line segment joining the points (-2,-3) and (3,7) is divided by the y – axis ? Also, find the co – ordinates of the point of division

to divide a line segment AB in the ratio 3:4 we draw a ray AX , so that angle BAX is an acute angle , and then mark the points on the ray AX at equal distances such that the minimum number of these points is ????

find the coordinates of the point equidistant from three given points A (5 , 1 ) , B (-3,-7 ) and C( 7, -1).

let the opposite angular points of a square ABCD be A(3,4) C(1,-1).find C and D

find the ratio in which the line 2x + 3y - 5 = 0 divideds the line segment joining the points (8,-9) and (2,1) . also find the coordinates of the point of division.

Four points A(6,3) , B(-3,5) , C(4,-2) , and D(x,3x) are given in such a way that

area of triangle DBC/area of triangle ABC =1/2. Find x

If G be the centroid of a triangle ABC, prove that, AB

^{2}+BC^{2}+CA^{2}=3(GA^{2}+GB^{2}+GC^{2})(C) ab = cd (D) ab=- cd

If A(1,2) , B(4,3 ) and C( 6,6) are the three vertices of a parallelogram ABCD , find the coordinates of the fourth vertex D

Find a relation between x and y such that the point P(x,y) is equidistant from the points A(7,1) and B(3,5) .^{th}of a school undertake to work for the campaign 'Say no to plastic' in the city. They took the map of the city and formed co-ordinate plane on it to divide their areas. Group A took the region covered between the co-ordinates(1,1) (-3,2) (-2,2) and (1,-3) taken in order. Find the area of the region covered by Group AThe age of the father is twice the sum of the ages of his two children.After,20 years , his age will be equal to the sum of the ages of his children.Find the age of the father

(a) a=2, b=0

(b) a=-2, b=6

(c) a=-2, b=0

(d) a=6, b=2

Q1) Prove that the points (a,0),(b,0), and (1,1) are collinear if 1/a + 1/b =1

Q2) Prove that the points (a,b), (c,d), and ( a-c,b-a) are collinear if ad=bc.

Q3) three consecutive vertices of a parallelogram ABCD are A (1,2) B (1,0) and C (4,0).Find the fourth vertex.

If the midpoints of sides of the triangle PQR are (1,2) (0,1) (1,0), then find the cordinates of thevertices of the triangle.

Q. Find the values of y for which the distance between the points P (2, - 3) and Q (10, y) is 10 units.

in what ratio does the x-axis divide the segment joining the points (-4,-6) and (-1,7), also find the coordinates of point of division

The vertices of a triangle ABC are A(1,2), B(4,6) C(6,14). AD is the bisector of the angle A meets BC at D. Find the coordinates of the point D.

find the circumcentre of the triangle whose vertices are (-2,-3), (-1,0), (7,-6)

A(6,1), B(8,2), C(9,4) are three vertices of a parallelogram ACBD. If E is midpoint of DC, find the area of ∆ADE.

If three points (x

_{1},y_{1}),(x_{2},y_{2}) and (x_{3},y_{3}) lie on the same line,prove that y_{2}-y_{3}/ x_{2}x_{3}+ y_{3}-y_{1}/ x_{3}x_{1}+ y_{1}-y_{2}/ x_{1}x_{2}= 0Find the point on Y-axis which is equidistant from the points (5,-2) and (-3,2)?

The base BC of an equilateral triangle ABC lies on y axis. The coordinates of pt. C are (0,-3). If the origin is the mid pt. of the base BC, find the coordinates of the pt. A and B and hance find the area of the triangle.

B-13 The equation of the diameter of the circle (x-2)

^{2}+(y+1)^{2}=16 which bisects the chord cut off by the circle on the line x-2y-3=0 is(A) x+2y=0 (B) 2x+y-3=0 (C) 3x+2y-4=0 (D) 3x-2y-4=0

Find the area of the quadrilateral whose vertices taken in order are (-4, -2), (-3, -5 ), (3, -2), and (2,3)........

show that the points (-3,5), (3,1), (0,3) and (-1,-4) do not form a quadrilateral

if a (-3 5),b (-1 1) and c(3 3) are the vertices of a triangle ABC, find the length of the median AD.also find the co-ordinates of the point which divides the AD in the ratio of 2:1

the line segment joining the points A ( 2 , 1 ) B ( 5 , -8 ) is trisected at the points p and q such that P is nearer to A . if P also lies on the line given by 2 x - y + k =0 , find the value of k.

the points (-a , -b) (0,0) (a,b) (a

^{2},ab) are :collinear

vertices of a parallelogrm

vertices of a rectangle

none of these

FIND THE RATIO IN WHICH THE Y- AXIS DIVIDES THE LINE SEGMENT JOINING THE POINTS ( 5 , -6 ) AND ( -1 , -4 ) .

for such a question i know that the ratio is taken as k : 1 . But what ratio should be taken if it is asked for x - axis ?

Is it the same ?

If R( x , y ) is a point on the line segment joining the points P( a , b ) and Q( b , a ) , then prove that x+y =a+b

using analytical geometry,prove that the diagonals of a rhombus are perpendicular to each other please help me guys?????

(i) the length of the arc (ii) area of the sector formed by the arc

(iii)area of the line segment formed by the corresponding chord.

Let D(3,-2),E(-3,1) and F(4,-3) be the midpoint of the sides BC,CA and AB respectively of

/ABC.Then find the coordinates of the vertices A,B and C.find the ratio in which point P(-1,y) lying on the line segment joining points A(-3,10) and B(6,-8) divides it. also find the value of y.

Find the area of the Quadrilateral ABCD whose vertices are A ( -3 , -1) , B (-2, -4) , C ( 4, -1) andD (3,4) . ..1.The points A(x

_{1},y_{1}),B(x_{2},y_{2}) and C(x_{3},y_{3}) are the vertices of triangle ABC.(1)The median from A meets BC at D.What are thEcoordinates of the point D?

(2)Find the coordinates of the point P on AD such that AP : PD = 2:1

(3)Find the coordinates of points Q and R on medians BE and CFrespectivelysuch that BQ : QE = 2:1 Aand CR : RF = 2 :1.

(4)What are the coordinates of the centroid of the triangle ABC?

Find the point on x-axis which is equidistant from the points (2,-5) and (-2,9)

if the points A(4,3) and B(x,5) are on the circle with centre O(2,3), find the value of x.

points A(-2, 0) and B(6. 0).

Find a point on y axis which is equidistant from the pts. A(6,5) and B(-4,3).

IN WHAT RATIO DOES THE LINE x-y-2=0 divide the line segment joining (3,-1) and (8,9) ?

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, − 1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

1- the perpendicular bisector of line segment joining the points a(1,5) b(4,6) cuts y axis at which point

2-if the point p (2,1)lies on the line segment joining points a(4,2 ) and b (8,4) then

a- ap=1/3ab , b- ap=pb, c- pb=1/3ab d- ap=1/2 ab choose the correct option

i m getting the relation ab=4 ab am i right or wrong plz specify this

3- show that a (-3,-1), b- (-4,-1), c(3,3) , d (4,3) r the vertices of rhombus i m not getting rhombus

Find the coordinates of the cicumcentre of the triangle whose vertices are (8,6), (8,-2) and (2,-2). Also find its circumradius.(plz explain step wise)Find the value of k if the points A(k+1, 2k), B(3k, 2k+3)and C (5k – 1, 5k) are collinear.

for what value of k are the points (k,2-2k) -k+1, 2k) and (-4-4k,6-2k ) are collinear .

The coordinate of two points A and B are (3,4) and (5,-2) respectively. Find the coordinate of point P if PA=PB. The area of triangle APB=10.

If two opposite vertices of a square are (5,4) and (1,-6), find the co ordinates of its remaining two vertices.

The vertices of a triangle are (2,a), (1,b) & (c

^{2},-3).the distance of the points p (2,3) from the x axis is