Question

Four friends A, B, C and D are playing in the park. They took one long rope and try to form a parallelogram. The position of A is (3, 2) and that of B is (1, 0). They took two more rope to form two diagonals and the ropes are intersecting at (2, –5). Now find coordinates of the other positions c and d

Answer 1

The vertices C is (1,-12) and D is (3,-10).

Step-by-step explanation:

Let the coordinates of C are (h,k) and that of D are (m,n).

Now, given that A(3,2) and B(1,0) are the coordinates of vertices of a parallelogram ABCD and the diagonals AC and BD intersect at the point (2,-5).

Therefore, the midpoint of A(3,2) and C(h,k) is (2,-5).

So, $\frac{3 + h}{2} = 2$

⇒ h = 1

And, $\frac{2 + k}{2} = - 5$

⇒ k = - 12

Again, the midpoint of B(1,0) and D(m,n) is (2,-5).

Hence, $\frac{m + 1}{2} = 2$

⇒ m = 3

And, $\frac{n + 0}{2} = - 5$

⇒ n = - 10

Therefore, the vertices C is (1,-12) and D is (3,-10). (Answer)