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

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:

  $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

→Slope of line AB is

$m_{1}=\frac{4-3}{1+3}=\frac{1}{4}$

→Slope of Line Y Z is:

$m_{2}=\frac{k-7}{-2+4}=\frac{k-7}{2}$

→Line AB and Line YZ are Perpendicular.

So,Product of their slopes = -1.

$m_{1}\times m_{2}= -1\\\\\frac{1}{4} \times \frac{k-7}{2}= -1\\\\ k-7= -8\\\\k=-8+7\\\\k=-1$

→  Y coordinate of point Z = -1

Option A: y=-1

Answer 2

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