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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.

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.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)

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

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

find the point which is three-fourth of the way from (3,1) to (-2,5)

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)

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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.

D(7,9) , E(1,1) and F(-1,-7) are the vertices of the triangle DEF . L(4,5) , M(-1,-3) , and N(2,1) are the mid points of DE , EF and FD respectively . prove that

area of triangle DEF/ area of triangle LMN =4/1

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 tplease givemeaningful step by step answers,not any similar link.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})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

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

the coordinates of A,B,C are (3,4) (5,2) and (x,y) respectively. if area of triangle ABC = 3, show that x+y = 10

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 k such that (k,2-2k) , (-4-k , 6-2k) and (-k+1 , 2k) are collinear

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

Q3.If the coordinate of point P and Q are (2,5) and (8,6) respectively. Find the coordinates of L such that PL/LQ = 2/5 ?

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.

The ordinate of a point is twice its abscissa. Find the coordinates of the point, if its distance from the point (4,3) is root 10 units.

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.

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.

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 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.

in what ratio does the pooint (-4,6) devides the line segment joining the point A(-6,10) and B(-7,4)

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.

Please and Thanks!

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 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.

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

Find the area of the Quadrilateral ABCD whose vertices are A ( -3 , -1) , B (-2, -4) , C ( 4, -1) andD (3,4) . ..Find the point on x-axis which is equidistant from the points (2,-5) and (-2,9)

Find the points of trisection of the line segment determined by (7,5) and (16, -1).

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

If the co-ordinates of the mid-points of the sides of triangle are (1,1), (2,-3), and (3,4), find its centroid.

Please clarify this doubt :

QUESTION :

FIND THE POINT ON THE X AXIS WHICH IS EQUIDISTANT FROM ( 2,-5) AND ( -2, 9 )

DOUBT :

THIS PROBLEM WHEN SOLVED CONSIDERING THE TWO PINTS GIVEN GIVEN AS P AND Q AND THE MID POINT AS R , WE GET PR = QR AND WE GET RESULT AS R = ( -7, 0 )

WHY DOES THE SECTION FORMULA REDUCED TO EQUIDISTANT FORMULA ( X1 + X2 )/ 2 SINCE M1 = M2 DOES NOT GIVE SAME ANSWER .

SO IS THE EQUIDISTANT FORMULA NOT VALID TO BE USED WHEN THE INTERSECTION IN ON THE AXIS ( X AXIS OR Y AXIS ).

THE SAME EQUIDISTANT FORMULA WORKS IN OTHER CASES, FOR EXAMPLE IN THE BELO W QUSETION ( TRISECTION ).

FIND THE COORDINATES OF THE POINTS OF TRISECTION OF THE LINE SEGMENT JOINING POINTS A( 2,-2), B(-7,4 ).

PLEASE CLARIFY IMMEDIATELY.

THANKS

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

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

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

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

And no links please

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)fint the points on x-axis which is at a distance of 2 route 5 from the point (7,-4). how many such points are thr.. ?

expertss plz help me wid this also.., have mA FA tmmrw

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 locus of point (a cosec θ + b cot θ.a cot θ + b cosec θ) 0 < θ < 2pi

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.

ABCDE is a polygon whose vertices are A(-1,0) ,B(4,0) ,C(4,4) ,D(0,7) , E(-6,2) . Find the area of the Polygon.Find the value of k if the points A(k+1, 2k), B(3k, 2k+3)and C (5k – 1, 5k) are collinear.

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

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