Find the distance from the point P(-3,5) to the midpoint of the line segment between A(5,-2) and...

Question:

Find the distance from the point P(-3,5) to the midpoint of the line segment between A(5,-2) and B(1,6).

Distance Between 2 Points:

To find the distance between 2 points, we can use euclidean distance. It not only works for 2D but also works for more than 2 dimensions. We need to find the distance between each dimension, take the square of each distance, sum them up, and take the square root at the end.

Answer and Explanation:

First, we should find the middle point, C, by averaging the values for x and y using the formula shown below where P is the middle point of M(a,b) and N(c,d).

Formula:

{eq}P = (\frac{a+c}{2}, \frac{b+d}{2}) {/eq}

Calculation:

{eq}C= (\frac{5+1}{2},\frac{-2+6}{2}) = (3,2) {/eq}

Then, we use the euclidean distance to find the distance between 2 points.

Formula:

{eq}d = \sqrt{(a-c)^2+(b-d)^2} {/eq}

Calculation:

{eq}d = \sqrt{(3-(-3))^2+(2-5)^2} = \sqrt{45} \approx 6.7 {/eq}


Learn more about this topic:

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How to Find the Distance Between a Point & a Line

from FTCE Mathematics 6-12 (026): Practice & Study Guide

Chapter 30 / Lesson 5
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