Question

(pls help me with this)

Answer 1

A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]

B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)

A. How to determine the mid point

• Coordinate of C = (4, 5)
• Coordinate of D = (p, q)
• Mid point =?

Mid point = (X , Y)

X = (x₁ + x₂) / 2

X = (4 + p) / 2

Y = (y₁ + y₂) / 2

Y = (5 + q) / 2

Thus,

Mid point = (X , Y)

Mid point = [(4 + p) / 2 , (5 + q) / 2]

B. How to determine the coordinates of D

• Mid point = (7, 1)
• Coordinates of D =?

Mid point = (7, 1) = (X , Y)

X = (4 + p) / 2

7 = (4 + p) / 2

Cross multiply

7 × 2 = 4 + p

14 = 4 + p

Collect like terms

p = 14 - 4

p = 10

Y = (5 + q) / 2

1 = (5 + q) / 2

Cross multiply

1 × 2 = 5 + q

2 = 5 + q

Collect like terms

q = 2 - 5

q = -3

Coordinates of D = (p, q)

Coordinates of D = (10 , -3)

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