# 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.

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}