How do you find the value of y so that the line through (-2,-1) and (10,y) is perpendicular to the line through (6,-2) and (5,7)?

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Answer 1 · 2017-07-30T16:59:49

$y=1/3.$

Let us call the given points (pts.) $A, B, C, and D,$ resp.

Then, we know that,

$"Line "AB bot" line "CD$

$iff" (slope of "AB)"(slope of "CD)=-1............(star).$

Here, slope of $AB=(y-(-1))/(10-(-2))=(y+1)/12,$ and,

slope of $CD=(7+2)/(5-6)=-9.$

Utilising these in $(star),$ we get,

$(y+1)/12*(-9)=-1 rArr 9y+9=12.$

$rArr y=3/9=1/3,$ is the Desired Value of $y.$