Question

Please help, asap thank you!

Answer 1

A)

`√(290)\approx 17.0\text{ units}`

B)

`√(53)\approx7.3\text{ units}`

Explanation:

To find the distance between any two points, we can use the distance formula:

`d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2`

Problem 1)

We have the two points (-4, 5) and (7, 18).

Let (-4, 5) be (x₁, y₁) and let (7, 18) be (x₂, y₂).

Substitute:

`d=√((7-(-4))^2+(18-5)^2)`

Evaluate:

`\begin{aligned}d&=√((11)^2+(13)^2)\\&=√(121+169)\\&=√(290)\approx17.0\end{aligned}`

Problem 2)

We have the two points (-2, -3) and (-4, 4).

Similarly, we will let (-2, -3) be (x₁, y₁) and (-4, 4) be (x₂, y₂).

Substitute:

`d=\sqrt{(-4-(-2))^2+(4-(-3))^2`

Evaluate:

`\begin{aligned}d&=√((-2)^2+(7)^2)\\&=√(4+49)\\&=√(53)\approx7.3\end{aligned}`