Question

The end of diagonals of a rhombus are (-5,2) and (1,6).If the coordinates of the 3rd vertex are (-6,10).what are the coordinates of the 4th vertex?

A. (2,-2)
B.(-8,0)
C. (4,8)
D. (-9,8)

Answer 1

Hi there!

Diagonals of a rhombus bisect each other.

This means th't both the diagonals must have the same mid-point.

Hence, the midpt. of the diagonal through vertices.

by Mid-point formula :-

∴ [
`\frac {-5 + 1}{2}`,
`\frac {2 + 6}{2}` ] = [
`\frac {-6 + x}{2}`,
`\frac {10 + y}{2}` ]

→ For x :--

=> - 6 + x = - 4

=> x = 6 - 4

=> x = 2

→ For y :--

=> 10 + y = 8

=> y = 8 - 10

=> y = -2

Therefore, Th' fourth vertex is (x, y) = (2, -2)

Hence,
Option [ A. ] : (2, -2) is Correct

~ Hope it helps!