Question

Find the distance from point A to XZ. Round your answer to the nearest tenth. (Explain please)

Answer 1

The distance from point A to the  segment XZ is equal the distance between points A and Y.

Why? Because AY is perpendicular to XZ. And this is the shortest distance.

The formula of a distance between two points:

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

We have A(3, 0) and Y(0, 1). Substitute:

$d=\sqrt{(0-3)^2+(1-0)^2}=\sqrt{(-3)^2+1^2}=\sqrt{9+1}=\sqrt{10}$

$\sqrt{10}\approx3.2$

Answer: d = 3.2

Answer 2

Answer:

3.2 units.

Step-by-step explanation:

We have been given an image on coordinate plane. We are asked to find the distance between point A to segment XZ.

We will use distance formula to solve our given problem.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since segment AY is perpendicular to segment XZ, so we will use points A and Y to find distance between point A to segment XZ.

Let point $(x_2,y_2)=(3,0)$ and $(x_1,y_1)=(0,1)$.

Substitute coordinates of both points in distance formula.

$D=\sqrt{(3-0)^2+(0-1)^2}$

$D=\sqrt{(3)^2+(-1)^2}$

$D=\sqrt{9+1}$

$D=3.16227766$

Round to nearest tenth:

$D=3.2$

Therefore, the distance from point A to segment XZ will be 3.2 units.