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Chapter 32: Problem 1025

What are the coordinates of the midpoint of a line segment joining \(\mathrm{P}(-2,1)\) and \(\mathrm{Q}(6,4) ?\)

Short Answer

Expert verified
The midpoint of the line segment joining P(-2, 1) and Q(6, 4) is M(2, 2.5).

Step by step solution

01

Identify the given coordinates for both points

We are given the coordinates for point P as (-2,1) and for point Q as (6,4).
02

Apply the midpoint formula

Use the midpoint formula to find the coordinates of the midpoint M: M = \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\)
03

Plug in the coordinates into the midpoint formula

Now, plug the coordinates of points P and Q into the formula: M = \(\left(\frac{-2 + 6}{2}, \frac{1 + 4}{2}\right)\)
04

Calculate the midpoint coordinates

Perform the calculations within the parentheses and divide by 2: M = \(\left(\frac{4}{2}, \frac{5}{2}\right)\)
05

Simplify the midpoint coordinates

Simplify the fractions: M = (2, 2.5)
06

Write the final answer

The coordinates of the midpoint of the line segment joining P(-2, 1) and Q(6, 4) are M(2, 2.5).

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