1) Find the midpoint for each set of points.
a) (4, 5) and (-6, 3)
Midpoint = ((4 + (-6))/2, (5 + 3)/2) = (-2/2, 8/2) = (-1, 4)
b) (-1, 5) and (2, -3)
Midpoint = ((-1 + 2)/2, (5 + (-3))/2) = (1/2, 2/2) = (0.5, 1)
2) Find the distance between each set of points.
a) (-2, 8) and (3, -7)
Distance = √[(3 - (-2))² + (-7 - 8)²] = √[(5)² + (-15)²] = √[25 + 225] = √250 = 5√10
b) (0, 0) and (4, 3)
Distance = √[(4 - 0)² + (3 - 0)²] = √[16 + 9] = √25 = 5
3) Find the midpoint and the distance between each pair of points in the graph given.
a) Points: (2, 2) and (5, 2)
Midpoint = ((2 + 5)/2, (2 + 2)/2) = (7/2, 4/2) = (3.5, 2)
Distance = √[(5 - 2)² + (2 - 2)²] = √[3² + 0²] = √9 = 3
b) Points: (-4, 3) and (4, 5)
Midpoint = ((-4 + 4)/2, (3 + 5)/2) = (0/2, 8/2) = (0, 4)
Distance = √[(4 - (-4))² + (5 - 3)²] = √[8² + 2²] = √[64 + 4] = √68 = 2√17
c) Points: (0, 3) and (2, -2)
Midpoint = ((0 + 2)/2, (3 + (-2))/2) = (2/2, 1/2) = (1, 0.5)
Distance = √[(2 - 0)² + (-2 - 3)²] = √[2² + (-5)²] = √[4 + 25] = √29
d) Points: (-3, 6) and (4, -4)
Midpoint = ((-3 + 4)/2, (6 + (-4))/2) = (1/2, 2/2) = (0.5, 1)
Distance = √[(4 - (-3))² + (-4 - 6)²] = √[7² + (-10)²] = √[49 + 100] = √149
Parent Tip: Review the logic above to help your child master the concept of distance on the coordinate plane worksheet.
