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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.

of Rose, Sunflower, Champa and Jasmine respectively as shown in the following figure. A fifth

student Eshan wanted to plant her flower in this area. The teacher instructed Eshan to plant

his flower plant at a point E such that CE: EB = 3 : 2.

Answer the following questions:

i. Find the coordinates of point E where Eshan has to plant his flower plant.

ii. Find the area of ECD.

iii. Find the distance between the plants of Ajay and Deepak.

iv. The distance between A and B is:

v. The distance between C and D is:

How to prove three points collinear by Section Formula

Library first to return a book and then reaches School directly whereas Pulkit went to Skate

Park first to meet his friend and then reaches School directly.

i. How far is School from their Home?

ii. What is the extra distance travelled by Ramesh in reaching his School?

iii. What is the extra distance travelled by Pulkit in reaching his School? (All distances are

measured in metres as straight lines)

iv. The location of the library is:

v. The location of the Home is:

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.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)

the distance of point 4,5 from the x axis

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

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

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

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

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.

the distance between 2x+4=0 and x-5=0 is ?

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 tfind points on x axis which are at distance of 5 units from the point A (5,-3).

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

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

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

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

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

^{2}+BC^{2}+CA^{2}=3(GA^{2}+GB^{2}+GC^{2})1. How many cubes will have one face painted only in Blue?

(a) 1 (b) 2 (c) 3 (d) 4 (e) 5

2. How many cubes will have one face painted only in Green?

(a) 1 (b) 2 (c) 3 (d) 4 (5)

3. How many cubes are formed in all?

(a) 16 (b) 24 (c) 27 (d) 32 (e) 48

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) .The 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

find the ratio in which the line segment joining the point A(3,-6) and B(5,3) is divided by x axis. also find the coordinate of the point of intersection.

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.

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

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

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.

Find 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.

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

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.

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.

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.

1. name the type of triangle pqr formed by the points p(√2,√2) , q(-√2,-√2) and r(-√6,√6)

2. abcd is a parallelogram with vertices a(x1,y1) b(

x2,y2) and c(x3,y3). find the coordinated of the fourth vertex d in terms of x1,x2,x3,y1,y2,y3

we were assigned 30 sums as homework.. i dint know how to solve these two out of them. please help me out....

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

Find the point on x axis which is equidistance from points (-2,5) (2,-3)?

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 ?

(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.

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) . ..If the Point P(m,3) lies on the line segment joining the points A(-2/5,6) and B(2,8),find the value of m.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.

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

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

The point R divides the line segment AB, where A (-4,0) and B (0,6) are such that AR=3/4AB. Find the coordinates of R.

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

the distance of the points p (2,3) from the x axis is

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 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.

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.

Find the value of k if P(4,-2 ) is the mid point of hte line segment joining the points A(5k, 3) and B(-k,- 7)

Find the value of k if the points A(k+1, 2k), B(3k, 2k+3)and C (5k – 1, 5k) are collinear.

The centre pf a circle is ( 2a -1 , 7) and it passes through the point ( -3 , -1 0 . If the diameter of the circle is 20 units , then find the value of a

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

: Using section formula, show that the points A (- 3, 1), B (1, 3) and C (- 1, 1) are collinear.