Question

09 - finding distance

1. find the distance between points a(3, 3) and b(0, -4)
2. find the distance between points t(6,4) and m(-1, -2)

to the nearest tenth.

Explanation:

Step1: Recall the distance formula

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

Step2: Solve for problem 1

For points \(A(3,3)\) and \(B(0,-3)\), \(x_1 = 3,y_1 = 3,x_2 = 0,y_2=-3\).
Substitute into the formula: \(d=\sqrt{(0 - 3)^2+(-3 - 3)^2}=\sqrt{(-3)^2+(-6)^2}=\sqrt{9 + 36}=\sqrt{45}=3\sqrt{5}\approx6.7\).

Step3: Solve for problem 2

For points \(T(6,4)\) and \(N(-1,-2)\), \(x_1 = 6,y_1 = 4,x_2=-1,y_2 = -2\).
Substitute into the formula: \(d=\sqrt{(-1 - 6)^2+(-2 - 4)^2}=\sqrt{(-7)^2+(-6)^2}=\sqrt{49+36}=\sqrt{85}\approx9.2\).

Answer:

1. The distance between \(A\) and \(B\) is approximately \(6.7\).
2. The distance between \(T\) and \(N\) is approximately \(9.2\).