Question

find the distance between each pair of points.

1. (-5, -7), (-4, 4)
2. (-6, 6), (-3, 5)

Explanation:

1) Distance between \((-5, -7)\) and \((-4, 4)\)

Step 1: Recall the distance formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-5,y_1 = - 7,x_2=-4,y_2 = 4\).

Step 2: Substitute the values into the formula

First, calculate \(x_2 - x_1=-4-(-5)=-4 + 5 = 1\) and \(y_2 - y_1=4-(-7)=4 + 7 = 11\).
Then, \(d=\sqrt{(1)^2+(11)^2}=\sqrt{1 + 121}=\sqrt{122}\)

2) Distance between \((-6, 9)\) and \((-3, 5)\)

Step 1: Recall the distance formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-6,y_1 = 9,x_2=-3,y_2 = 5\).

Step 2: Substitute the values into the formula

Calculate \(x_2 - x_1=-3-(-6)=-3 + 6 = 3\) and \(y_2 - y_1=5 - 9=-4\).
Then, \(d=\sqrt{(3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

Answer:

s:

1. \(\sqrt{122}\)
2. \(5\)