The coordinates of point Z is (-5/7, 16/7)
Calculating the midpoint of a line using a ratio
The formula for calculating a coordinate points using the points (-5, -2) and point P is located at (1, 4) in the ratio 2:5 is expressed as:
Z (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}
Substitute the coordinates and ratios to have;
Z (x, y) = {(2(-5)+5(1))/2+5, (2(-2)+5(4))/2+5}
Z(x, y) = {-10+5/7, -4+20/7}
Z(x, y) = (-5/7, 16/7)
Hence the coordinates of point Z is (-5/7, 16/7)
Learn more on midpoint here; https://brainly.com/question/5566419
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