Question

Determine the value of A so that the line with the equation is 2x + y = 2 is perpendicular toanother line containing the points (A, -3) and (-2, 4).

Answer 1

the equation of the line is

2x + y = 2

y = -2x + 2

so the slope is,

m = -2

slope of the line perpendicular to this line is

m = 1/2

the two points are (A, -3) and (-2, 4).

also, the slope is

$m=\frac{4-(-3)}{-2-A}$

put m = 1/2

$\begin{gathered} \frac{1}{2}=\frac{7}{-2-A} \\ -2-A=14 \\ A=-2-14 \\ A=-16 \end{gathered}$

so the answer is A = -16