Answer:
w is -3
Explanation:
A line with a perpendicular slope with have a slope that is the negative inverse of the reference line. If the reference line is -(2/3), the perpendicular line will have a slope of (3/2).
The line formed by ab: y = (3/2)x + b
We have one given point on line ab with one coordinate known, (3,4), so let's use it to find b:
y = (3/2)x + b
4 = (3/2)*3 + b for (3,4)
4 = (9/2) + b
b = 4 - (9/2)
b = - 0.5
The equation is y = (3/2)x - 0.5
The slope of (3/2) is equal to the Rise/Run of two points on the line: (3,4) and (w,-5):
Rise = (4 - (-5)) = 9
Run = (3 - w)
Slope = 9/(3-w)
(3/2) = 9/(3-w)
(3/2)(3-w) = 9
(9/2) - (3/2)w = 9
9 - 3w = 18
-3w = 9
w = -3
Point b is (-3, -5)
See attached graph.