Question

Three vertices of parallelogram WZXY are W(-5, 2), X(2, 4) and Z(-7, -3). Find the coordinated of the vertex, Y.

Answer 1

`Y = (4,9)`

Explanation:

Given

`W(x_1,y_1) = (-5, 2)`

`Z(x_4,y_4) = (-7, -3)`

`X(x_2,y_2) = (2, 4)`

Required

Find Y

To do this, we make use of the mid-point formula

i.e.

`M = (1)/(2)(x_n+x_m,y_n+y_m})`

WX and ZY are the diagonals of the parallelogram.

The mid-point of WX is:

`M = (1)/(2)(-5+2,2+4)`

`M = (1)/(2)(-3,6)`

The mid-point of ZY is:

`M = (1)/(2)(-7+x,-3+y)`

Equate both values of M

`(1)/(2)(-3,6) = (1)/(2)(-7+x,-3+y)`

Multiply both sides by 2

`(-3,6) = (-7+x,-3+y)`

By comparison:

`-7 + x = -3`

`-3 + y = 6`

`-7 + x = -3`

`x = 7 -3`

`x = 4`

`-3 + y = 6`

`y = 6 +3`

`y = 9`

Hence:

`Y = (4,9)`