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.#