Question

Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. Round the distance to the nearest tenth. P(−4, 1) and Q(0, 7) The midpoint is at M( , ). Question 2 The distance between the two points is about units.

Answer 1

Question 1. Midpoint

Answer: M(-2,4)

Explanation:

1) The coordinates of the midpoint, M (x,y) between two points (x₁,y₁) and (x₂, y₂) are:

x = (x₁ + x₂) / 2 and y = (y₁ + y₂) / 2

2) Replacing the coordinates of the given points P (-4, 1) and Q (0,7) you get:

x = (- 4 + 0) / 2 = - 2, and
y = (1 + 7) / 2 = 4

So, the answer is M (-2,4)


Question 2: The distance between the two midpoints is:

Answer: 7.21


Explanation:

1) Use the formula of distance, which is an application of Pythagora's theorem:

d² = (x₂ - x₁)² + (y₂ - y₁)²

2) Substitute values:

d² = (0 - (-4))² + (7 - 1)² = 4² + 6² = 16 + 36 = 52 ⇒ d = √52 ≈ 7.21