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
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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