Question

A. The point-slope form of the equation of a line is y ? y1 = m(x ? x1), where m is the slope and (x1, y1) is a point on the line. Write the equation of the line in point-slope form perpendicular to the graph of y = 1/2x -7 passing through the point (6, 5).
B. Write an equation of the perpendicular bisector of JK, where J = (?8, 4) and K = (4, 4).

Can you show work please.

Answer 1

Answer:

A.

$y - 5 = -2(x-6)$

Negative reciprocal gives you the perpendicular slope so negative reciprocal of 1/2 is -2.

Then apply point-slope form.

B. The answer is x = 6.

The midpoint of JK is

$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{8+ 4}{2}, \frac{4 + 4}{2} \right) = \left(6,4\right)$

The line that goes through JK is just a horizontal line $y = 4$ because the y-coordinate does not change. So its perpendicular bisector is the vertical line that goes through the x-coordinate of the midpoint, that is, $x = 6$.