Question

welcome to geometry honors. please complete this find the distance between each pair of points. 1) (-5, -7), (-4, 4) 3) (2, 7), (8, 7)

Explanation:

Problem 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, \(d=\sqrt{(1)^2+(11)^2}=\sqrt{1 + 121}=\sqrt{122}\)

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, \(x_1 = 2\), \(y_1=7\), \(x_2 = 8\), \(y_2=7\).

Step 2: Substitute the values

Calculate \(x_2 - x_1=8 - 2=6\) and \(y_2 - y_1=7 - 7 = 0\). Then, \(d=\sqrt{(6)^2+(0)^2}=\sqrt{36+0}=\sqrt{36}=6\)

Answer:

\(\sqrt{122}\)

Problem 3: Distance between \((2,7)\) and \((8,7)\)