std 8 algebraic expressions
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PERPENDICULAR LINES
Michow D. asked • 02/24/16
A line m goes through the point (4, -3) and is perpendicular to the line 3x + 2y = 9. The point (k, k +3) lies on this perpendicular line m. Find the value of k
know there's a formula but I can't think of what
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David W. answered • 02/24/16
Experienced Prof
The equation of a first line is given in Standard Form (Ax+By=C): 3x + 2y = 9.
The line m is perpendicular to it; that means that line m has a slope that is the negative reciprocal of the slope of the first line. The slope of the first line (-A/B) is -3/2 and slope of the perpendicular line m is 2/3. This makes the equation line m:
2x - 3y = D and we need point (4,-3) to determine D.
2(4) - 3(-3) = D
8 + 9 = D
17 = D
The equation of line m is 2x - 3y = 17
"The point (k,k+3) lies on this perpendicular line m. Find the value of k."
2(k) - 3(k+3) = 17
2k -3k -9 = 17
-k = 26
k = -26
Let's check that (k,k+3) [that is, (-26,-23)] is on the perpendicular line m:
2(-26) - 3(-23) = 17 ?
-52 + 69 = 17 ?
17 = 17 ?yes