Question

Homework due at 12:00
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Answer 1

k = - 7.5

Explanation:

Slope "m" of a line through points

(
`x_(1)` ,
`y_(1)` )

(
`x_(2)` ,
`y_(2)` )

is m =
`(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)` =
`(10-7)/(2-0)` =
`(3)/(2)`

Slope of perpendicular line through points (3, 5) and (k, 12) is
`m_(2)` =
`-(2)/(3)`

or
`m_(2)` =
`(12-5)/(k-3)`

`(7)/(k-3)` =
`-(2)/(3)`

2(k - 3) = - 21

k - 3 = - 10.5

k = - 7.5