Question

Find the distance between$\left(3,-6\right)$ and$\left(1,4\right)$ on a coordinate grid. Round to the nearest tenth.

1. $8.1$
2. $8.5$
3. $9.6$
4. $10.2$

Short answer

Option D is the correct answer.

Step-by-step solution

Step 1. Define the coordinates of a point.

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.

Step 2. Determine the distance between two points x1, y1 and x2, y2 on a coordinate grid.

The distance between the two points$\left(x_1,y_1\right)$ and$\left(x_2,y_2\right)$ is

$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\mathrm{.............}\left(1\right)$

Step 3. Determine the distance between two points 3, −6 and 1, 4 on a coordinate grid.

Use (1).

The distance between the two points$\left(3,-6\right)$ and$\left(1,4\right)$ is

$$\begin{gathered} =\sqrt{{\left(1-3\right)}^2+{\left(4-\left(-6\right)\right)}^2} \\ =\sqrt{{\left(-2\right)}^2+{\left(4+6\right)}^2} \\ =\sqrt{{\left(-2\right)}^2+{\left(10\right)}^2} \\ =\sqrt{4+100} \\ =\sqrt{104} \\ \approx 10.2 \end{gathered}$$

Hence, the distance between the two points$\left(3,-6\right)$ and$\left(1,4\right)$ on a coordinate grid is 10.2.

Therefore option D is the correct answer.