Question

Homework due at 12:00 I Need Help

Answer 1

Answer:

k = - 7.5

Step-by-step explanation:

Slope "m" of a line through points

( $x_{1}$ , $y_{1}$ )

( $x_{2}$ , $y_{2}$ )

is m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

Slopes of perpendicular lines are opposite reciprocal: $m_{1}$ $m_{2}$ = - 1

~~~~~~~~~~~~~~~

The slope of a line through points (0, 7) and (2, 10)

$m_{1}$ = $\frac{10-7}{2-0}$ = $\frac{3}{2}$

Slope of perpendicular line through points (3, 5) and (k, 12) is $m_{2}$ = $-\frac{2}{3}$

or $m_{2}$ = $\frac{12-5}{k-3}$

$\frac{7}{k-3}$ = $-\frac{2}{3}$

2(k - 3) = - 21

k - 3 = - 10.5

k = - 7.5