If Two Vertices of a Parallelogram Are (3, 2) (-1, 0) and the Diagonals Cut at (2, -5), Find the Other Vertices of the Parallelogram. - Mathematics

If two vertices of a parallelogram are (3, 2) (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.

Solution

We have a parallelogram ABCD in which A (3, 2) and B (-1, 0) and the co-ordinate of the intersection of diagonals is M (2,-5).

We have to find the coordinates of vertices C and D.

So let the co-ordinates be C(x_1, y_1) and D(x_2, y_2)

In general to find the mid-point P(x,y) of two points A(x_1, y_1) and B(x_2, y_2) we use section formula as,

P(x,y) = ((x_1 + x_2)/2,(y_1 + y_2)/2)

The mid-point of the diagonals of the parallelogram will coincide.

So,

Therefore

((3 + x_1)/2, (2 + y_1)/2) = (2,-5)

Now equate the individual terms to get the unknown value. So,

x = 1

y = -12

So the co-ordinate of vertex C is (1,-12)

Similarly,

Co-ordinate of mid-point of BD = Co-ordinate of M

Therefore

((-1+ x_2)/2,(0 + y_2)/2) = (2,-5)

Now equate the individual terms to get the unknown value. So,

x = 5

y = -10

So the co-ordinate of vertex C is (5,-10)

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RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Exercise 6.3 | Q 46 | Page 30