Which point is on the line that passes through point z and is perpendicular to line ab? a. (-4,1) b. (1,-2) c. (2,0) d. (4,4)

The point is on the line that passes through point Z and is perpendicular to line AB is (-4,1) and this can be determined by using the slope-intercept form of the line.

Given :

Points  ---  A(-2,4), B(0,-4), and Z(0,2)

First, determine the slope of line AB. The slope of line AB is given by:

m = -4

The slope of the line which is perpendicular to the line AB is given by:

mm' = -1

m' = 1/4

Now, the equation of the line perpendicular to the line AB is given by:

4y = x + 8   --- (1)

Now, the point which satisfies the equation (1) is (-4,1). Therefore, the correct option is A).

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step-by-step explanation: