Question

A line L has a slope of -2 and passes through the point (r,-3). a second line, K is perpendicular to L at (a,b) and passes through the point (6, r). find a in terms of r.

I find the slope of K is 1/2 and i know (a, b) is the shared solution to both lines but idk what to do next.

Answer 1

Line L:
y = -2 x + c
-3 = -2 r + c
2 r = c+3
c = 2 r -3
so
y = -2x +2r -3

Line K
perpendicular so slope = -1/-2 = 1/2
y = (1/2) x + d
r = 3 + d
d = r-3
or
y = (1/2) x + r-3
-------------------------------
now they go through (a,b)
y = - 2 x + 2r - 3 --> b = -2 a +2r - 3
y = (1/2) x+ r - 3 --> b = a/2 +r - 3
------------------------------------------ subtract
0 = -2.5 a + r
a = 2 r / 5

Answer 2

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