Answer and Step-by-step explanation in one:
(4+9)/(-2-1) = 13/-3 = -13/3
y=-13x/3 + b
4=26/3 + b
b = 4-26/3 = (12-26)/3 = -14/3
y=-13x/3 -14/3 is the line through the two given points
find the line perpendicular and through (14,-6)
y=3x/13 + b, plug in the point to find b
-6 = 3(14)/13 + b
b = -6 -42/13 = -78/13 - 42/13 = -120/3
y= 3x/13 - 120/13
find the intersection point of the two lines, set them equal
3x/13 -120/13 = -13x/3 - 14/3
multiply by 39
9x - 360 = -169x - 182
178x = 360-182 = 178
x = 1
y= -27/3=-9
the point is (1,-9)
calculate the distance from (1,-9) to (14,-6)
d^2 = 9+169 = 178
d = sqr178 = about 13.34