Question

find the distance between the points.

Explanation:

Step1: Identify coordinates

For the first graph: \(P_1(-5,4)\), \(P_2(4,1)\)
For the second graph: \(P_1(4,4)\), \(P_2(1,-4)\)
For the third graph: \(P_1(-2,3)\), \(P_2(-5,-4)\)
For the fourth graph: \(P_1(4,-4)\), \(P_2(-1,-2)\)

Step2: Apply distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

• First graph:

\(d=\sqrt{(4 - (-5))^2+(1 - 4)^2}=\sqrt{(4 + 5)^2+(-3)^2}=\sqrt{81 + 9}=\sqrt{90}=3\sqrt{10}\)

• Second graph:

\(d=\sqrt{(1 - 4)^2+(-4 - 4)^2}=\sqrt{(-3)^2+(-8)^2}=\sqrt{9 + 64}=\sqrt{73}\)

• Third graph:

\(d=\sqrt{(-5 - (-2))^2+(-4 - 3)^2}=\sqrt{(-5 + 2)^2+(-7)^2}=\sqrt{9 + 49}=\sqrt{58}\)

• Fourth graph:

\(d=\sqrt{(-1 - 4)^2+(-2 - (-4))^2}=\sqrt{(-5)^2+(2)^2}=\sqrt{25 + 4}=\sqrt{29}\)

Answer:

First graph: \(3\sqrt{10}\)
Second graph: \(\sqrt{73}\)
Third graph: \(\sqrt{58}\)
Fourth graph: \(\sqrt{29}\)