One endpoint of a line segment is (8, −1). The point (5, −2) is one-third of the way from that endpoint to the other endpoint. Find the other endpoint

Answer:The other endpoint is (-4, -5)Step-by-step explanation:We know the formula for the coordinates of the point dividing the line segment in the ratio of a : b is x = x' + [tex]\frac{a}{a+b}(x"-x')[/tex]y = y' + [tex]\frac{a}{a+b}(y"-y')[/tex] Now we plug in the values of endpoints (8, -1) and (x, y) with a point (5, -2) dividing the segment in 1 : 3 ratio.5 = 8 + [tex]\frac{1}{1+3}(x-8)[/tex] 5 - 8 = [tex]\frac{x-8}{4}[/tex](x - 8) = -3×4 = -12x = -12 + 8 = -4Similarly, -2 = -1 + [tex]\frac{1}{1+3}(y+1)[/tex]-2 + 1 = [tex]\frac{1}{4}(y+1)[/tex]y + 1 = -1(4)y + 1 = -4 y = -1 - 4 = -5Therefore, another endpoint of the segment is (-4, -5).