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anonymous
 4 years ago
In the xy plane, the points with coordinates (0,5) and (6,2) lie on line L. Line P contains the points with coordinates (5,0) and is perpendicular to Line L. What is the xcoordinate of the point where L and P intersect?
anonymous
 4 years ago
In the xy plane, the points with coordinates (0,5) and (6,2) lie on line L. Line P contains the points with coordinates (5,0) and is perpendicular to Line L. What is the xcoordinate of the point where L and P intersect?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0For Line L: \[y=mx+b\] You're given the yintercept which is the 5, so \[y=mx5\] Use the other point on L to get the gradient (m) but substituting in the point for x & y, & solve to get m: \[2=m*65\]\[2 = 6m5\]\[2+5=6m\]\[3=6m\]\[m=1/2\]Given that the line P is perpendicular to the line L, the gradient of line P must be 2 (opposite sign & reciprocal value to line L), so equation of Line P: \[y=2x+b\]substitute the point you're given (that is (5,0) to find the required value for b, which is the yintercept of the line P. you get\[0=2*5 + b\]\[0=10+b\]\[b=10\]Line P is \[y=2x10\]To find the intersection, equate the two lines and solve to find x\[x/25 = 2x10\]\[x10 = 4x20\]\[5x = 10\]\[x=2\]
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