Mathematics 2011 JAMB Past Questions - Question 32: The midpoint of P(x,y) and Q(8,6) is (5,8).find x and y

Correct Answer

A

Explanation

p (x,y) Q (8,6)midpoint = (5,8)x + 8 /2 = 5y + 6 /2 = 8x +8 = 10x =10 -8 = 2y+6 =16y = 16 -6 =10therefore P(2,10)To find the values of x and y, we can use the midpoint formula:The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)In this case, we have the midpoint (5, 8) and one of the points (8, 6) as Q.Using the midpoint formula, we can set up the following equations:(5, 8) = ((x + 8)/2, (y + 6)/2)Simplifying, we have:5 = (x + 8)/28 = (y + 6)/2To solve for x, we can multiply both sides of the first equation by 2:10 = x + 8Subtracting 8 from both sides, we get:2 = xTo solve for y, we can multiply both sides of the second equation by 2:16 = y + 6Subtracting 6 from both sides, we get:10 = yTherefore, the values of x and y are x = 2 and y = 10.