for the p(-15,10) and (-8,13) find the distance d(p,q) and the coordinates of the midpoint m of the segment pq

Answer 1

Let Point p be Point 1 and Point q be Point 2, then x₁ = -15 and y₁ = 10, x₂ = -8 and y₂ = 13

The distance formula is:

d = square root [(y₂ - y₁)² + (x₂ - x₁)²] so the distance d = square root [(13 - 10)² + (-8 - -15)²] = square root(3² + 7²) = square root (9 + 49) = square root(58) = approx 7.62

The midpoint formula for the midpoint (x_m, y_m) is x_m = (x₁ + x₂)/2 and y_m = (y₁ + y₂)/2 so x_m = (-15 + -8)/2 = -23/2 = -11.5 and y_m = (10 + 13)/2 = 23/2 = 11.5 so (x_m, y_m) = (-11.5, 11.5)