Which point is on the line that passes through point Z and is perpendicular to line AB?

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The picture in the attached figure we know that point A( -2,4) point B(0,-4) point Z(0,2) step 1 find the slope line AB m=(y2-y1)/(x2-x1)----> m=(-4-4)/(0+2)-----> m=-8/2---> m=-4 step 2 find the slope of the line perpendicular to AB if two lines are perpendicular  so m1*m2=-1 m1=-4 m2=1/4 step 3 find the equation of the line perpendicular to AB that passes through point Z m2=1/4  point z (0,2) y-y1=m*(x-x1)----> y-2=(1/4)*(x-0)---> y=0.25*x+2 step 4 analyze each point case a) (-4,1) for x=-4 y=0.25*-4+2----> y=1 1 is equal to 1-------> this point is on the line case b) (1,-2) for x=1 y=0.25*1+2----> y=2.25 2.25 is not -2-------> this point is not on the line case c) (2,0) for x=2 y=0.25*2+2----> y=2.5 2.5 is not 0-------> this point is not on the line case d)(4,4) for x=4 y=0.25*4+2----> y=3 3 is not 4-------> this point is not on the line   the answer is the point (-4,1)


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