Question

AB contains the points A(–3, 3) and B(1, 4). YZ contains the points Y(–4, 7) and Z(–2, y). AB and YZ are perpendicular. Find the value of the y-coordinate of point Z.

A.
y = –1
B.
y = 1
C.
y = 8
D.
y = 15

Answer 1

The correct answer is D to the question that you are asking

Answer 2

Answer with explanation:

Coordinates of A and B are which forms a Line = A (-3,3) and B (1,4).

Line Y Z ,contains the points , Y (-4,7) and Z (-2,y).

let, y=k.

→Slope of Line joining two points is given by:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

→Slope of line AB is

`m_(1)=(4-3)/(1+3)=(1)/(4)`

→Slope of Line Y Z is:

`m_(2)=(k-7)/(-2+4)=(k-7)/(2)`

→Line AB and Line YZ are Perpendicular.

So,Product of their slopes = -1.

`m_(1)* m_(2)= -1\\\\(1)/(4) * (k-7)/(2)= -1\\\\ k-7= -8\\\\k=-8+7\\\\k=-1`

→ Y coordinate of point Z = -1

Option A: y=-1