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Syeda
answered
1 year(s)
, 8 month(s) ago

To find 4th vertex of a parallelogram

Given three of vertices of a parallelogram are A(1,2), B (4,3), C (6,6).

Let the coordinates of fourth vertex be D (x, y)

In a parallelogram, diagonals bisect each other.

He

...- 2 Answers
- 4 Likes
- 66150 Views

Syeda
answered
1 year(s)
, 8 month(s) ago

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

Answer.

Let the point of x-axis be P(x, 0)

Given A(2, -5) and B(-2, 9) are equidistant from P

That is PA = PB

Hence PA
^{2} = PB
^{2} → (1)

Distan...

- 2 Answers
- 3 Likes
- 57810 Views

Syeda
answered
1 year(s)
, 7 month(s) ago

Ratio in which the line segment joining two points divided by x-axis

Answer.

Let the point on X-axis be
_{} since the y-coordinate is always zero on X-axis.

Given A(2, 3) and B(5, 6)

Let P divides the line segment joining the poin...

- 2 Answers
- 1 Like
- 51490 Views

Syeda
answered
1 year(s)
, 8 month(s) ago

If two vertices of an equilateral triangle be (0,0), (3,√3), find the third vertex.

Answer.

Two vertices of an equilateral triangle are (0, 0) and (3, √3).

Let the third vertex of the equilaterla triangle be (x, y)

Distance between (0, 0) and (x,...

- 2 Answers
- 4 Likes
- 46065 Views

Syeda
answered
1 year(s)
, 8 month(s) ago

Find the coordinates of the points of trisection of the line segment joining the points.

Sol:

Given line segment joining the points A(1,-2)and B(-3,4)

Let P and Q be the points of trisection of AB i.e., AP = PQ = QB

Therefore, P divides AB internally in the ratio 1 : 2.<

...- 2 Answers
- 2 Likes
- 41921 Views

Syeda
answered
1 year(s)
, 8 month(s) ago

Find the third vertex of the equilateral triangle.

Sol:

Two vertices of an equilateral triangle are (3, 4) and (-2, 3)

Let the third vertex of the triangle be (x, y)

Distance between (3, 4) and (-2, 3)

=√[(-2-3)
^{2} + (...

- 2 Answers
- 2 Likes
- 35174 Views

Syeda
answered
1 year(s)
, 8 month(s) ago

Find the coordinates of the circumcentre of the triangle.

Answer.

Let the coordinates of the circumcentre of the triangle be (x, y).

Circumcentre of a triangle is equidistant from each of the vertices.

Distance between (8, 6) an...

- 2 Answers
- 6 Likes
- 30153 Views

Ramesh
answered
3 year(s)
, 10 month(s) ago

If a point(x,y) is equidistant from the points (a+b, b-a) & (a-b, a+b), then prove bx = ay.

Distace between the points (x, y) and (a+b, b-a) & (a-b, a+b) is equal

⇒ √{[x - (a + b)]
^{2} + [y - (b -a)]
^{2}} = √{x - (a - b)]
^{2} + [y - (a + b)]
^{2}...

- 1 Answer
- 4 Likes
- 27893 Views

Syeda
answered
1 year(s)
, 7 month(s) ago

what point on x axis is equidistant from the points A(7,6) and B(-3,4) ?

Given points A(7,6) and B(-3,4)

Let the point be P(x,0) [we know that point on x-axis is (x,0)]

So, AP=PB and AP
^{2}=PB
^{2}

⇒(x-7)
^{2}+(0-6)
^{2}...

- 2 Answers
- 4 Likes
- 23439 Views

Agam
answered
1 year(s)
, 6 month(s) ago

If the points A(4, 3) and B(x, 5) lie on the circle

Given centre of circle is O(2, 3)

Points on the circle are A(4, 3) and B(x, 5)

OA =OB (Radii) à (1)

Recall the distance between two points formula�

Squaring on both the...

- 2 Answers
- 2 Likes
- 20060 Views

Agam
answered
1 year(s)
, 6 month(s) ago

Coordinates of points of trisection

Solution:

�

Given coordinates are� �and�

Trisection means dividing a line segment in three equal parts or dividing a line segment� in the ratio 1:2 and 2:1 internally.

Case (i):...

- 2 Answers
- 1 Like
- 16654 Views

Raghunath
answered
3 year(s)
, 11 month(s) ago

Show that the points (a,b+c), (b,c+a), (c,a+b) are collinear.

Any two points of sum is equal to the third then it must be a collinear.

- 2 Answers
- 0 Like
- 16269 Views

Agam
answered
1 year(s)
, 6 month(s) ago

Q--- Find the value of k if the points A(2,3) ,B(4,k) and C(6,-3) are collinear.

Given that A, B and C are collinear Hence ar(DABC) = 0

- 2 Answers
- 1 Like
- 16262 Views

Ramesh
answered
4 year(s)
ago

Prove that the given points are the vertices of a parallelogram.

Let the points (4, 5) (7, 6) (4, 3) (1, 2) represent the points A, B, C and D.

AB = √[(7 - 4)
^{2} + (6 - 5)
^{2}] = √(9 + 1) = √10

BC = √[(4 - 7)
^{2} + (3 -...

- 1 Answer
- 1 Like
- 15598 Views

Agam
answered
1 year(s)
, 4 month(s) ago

Midpoints of triangle are given find its sides

Let the vertices of the triangle are A(x1, y1), B(x2, y2), C(x3, y3)

Draw DE, DF, FE and BF

��

�

As D and F are mid points of AB and AC

∴�DF || BE

E and F are mi...

Asked by Adityabaweja

Feb 29

- 2 Answers
- 1 Like
- 14670 Views

Raghunath
answered
3 year(s)
, 11 month(s) ago

How to derive the section formula?

Consider any two points A (
*x*
_{1},
*y*
_{1}) and B (
*x*
_{2},
*y*
_{2}) and assume that P (
*x*,
*y*) divides AB internally in the rat...

Asked by Neeraja Babu

Feb 12

- 1 Answer
- 0 Like
- 13356 Views

Ramesh
answered
4 year(s)
, 10 month(s) ago

Vertices of an isosceles right angled triangle.

Sol:

Vertices of the triangle are A(-3, 0), B(1, -3), C(4, 1)

Distance between two points = (x
_{2} - x
_{1})
^{2}+(y
_{2 }- y
_{1})
^{2}...

- 1 Answer
- 1 Like
- 13145 Views

Agam
answered
1 year(s)
, 6 month(s) ago

Line segment divided by the Y-axis

Solution:

�

Let the point on Y-axis be� ����[Since on Y-axis x-coordinate is zero]

Let the Y-axis divide the given points� �in the ratio� �

Therefore the coordinates of P are giv...

- 2 Answers
- 1 Like
- 12838 Views

Raghunath
answered
4 year(s)
, 1 month(s) ago

How to derive the formula of centroid from section formula.

Sol:

Let centroid of the triangle the coordinates of whose vertices are given by A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) respectively.

- 1 Answer
- 0 Like
- 10597 Views

Ramesh
answered
4 year(s)
, 1 month(s) ago

Determine the ratio in which the point P divides AB.

Sol:

Let the ratio in which the point P divides the line segment joining the points A(-4, 3) and B(2, 8) be 1:k.

y-coordinate of point P =

[(8 + 3k) / (1 + k)] = 6...

- 1 Answer
- 0 Like
- 10258 Views

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