Determine the value of r such that the line through (5, r) and (2, 3) is perpendicular to the line y = 2x - 4

a. r = 1.5

b. r = 9

c. r = - 3

d. r = 4.5

Hello!

The line through (x1, y1) and (x2, y2) has the slope m1 = (y2-y1)/(x2-x1).

The line y = 2x - 4 has the slope m2 = 2.

For these lines to be perpendicular, m1 must be equal to -1/m2 = -1/2.

Here m1 = (3 - r)/(2 - 5) = -(3-r)/3 = -1 + r/3 = -1/2.

Therefore r/3 = 1 - 1/2 = 1/2 and r = 3/2 = 1.5, the a) option.

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