SOLUTION: A line has a y-intercept of 8 and an x-intercept of -12. what is the shortest distance from the origin to this line, to the nearest tenth?

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Question 1083157: A line has a y-intercept of 8 and an x-intercept of -12. what is the shortest distance from the origin to this line, to the nearest tenth?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A line has a y-intercept of 8 and an x-intercept of -12.
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m=8%2F12=2%2F3;
y=%282%2F3%29x%2B8------equation for the described given line


Line from the origin (0,0), perpendicular to given line:
y=-%283%2F2%29x


Their intersection
%282%2F3%29x%2B8=-%283%2F2%29x
%282%2F3%2B3%2F2%29x=-8
%284%2F6%2B9%2F6%29x=-8
%2813%2F6%29x=-8
x=-8%286%2F13%29
x=-48%2F13
-
y=-%283%2F2%29%28-48%2F13%29
y=%283%2A48%29%2F%282%2A13%29
y=3%2A24%2F13
y=72%2F13
-

Distance from origin
sqrt%28%2848%2F13%29%5E2%2B%2872%2F13%29%5E2%29

%281%2F13%29sqrt%2848%5E2%2B72%5E2%29

%281%2F13%29sqrt%287488%29
highlight%28%281%2F13%29%2A24%2Asqrt%2813%29%29






-
7488
832*9
4*208*9
4*4*52*9
4*4*4*13*9