Question

Find the coordinates of the missing endpoint if B is the midpoint of AC.

33. C(-5, 4), B(-2,5)
34. A(1,7), B(-3,1)
35. A(-4, 2), B(6, -1)
37. A(4,-0.25), B(-4, 6.5)
36. C(-6, -2), B(-3,-5)
38. C(2,-6), B(3,4)

Answer 1

Explanation:

the midpoint B = (xb, yb) between A (xa, ya) and C (xc, yc) is always

(xb, yb) = ((xa + xc)/2, (ya + yb)/2)

33.

(xa + -5)/2 = -2

xa - 5 = -4

xa = 1

(ya + 4)/2 = 5

ya + 4 = 10

ya = 6

A = (1, 6)

34.

(1 + xc)/2 = -3

1 + xc = -6

xc = -7

(7 + yc)/2 = 1

7 + yc = 2

yc = -5

C = (-7, -5)

35.

(-4 + xc)/2 = 6

-4 + xc = 12

xc = 16

(2 + yc)/2 = -1

2 + yc = -2

yc = -4

C = (16, -4)

36.

(xa + -6)/2 = -3

xa - 6 = -6

xa = 0

(ya + -2)/2 = -5

ya - 2 = -10

ya = -8

A = (0, -8)

37.

(4 + xc)/2 = -4

4 + xc = -8

xc = -12

(-0.25 + yc)/2 = 6.5

-0.25 + yc = 13

yc = 13.25

C = (-12, 13.25)

38.

(xa + 2)/2 = 3

xa + 2 = 6

xa = 4

(ya + -6)/2 = 4

ya - 6 = 8

ya = 14

A = (4, 14)