9 of 159 of 15 Items Question Lulu marks the points (9,2) and (3,6) on the coordinate plane. What is the distance between these two points, rounded to the nearest tenth of a unit?(1 point) Responses 10.0 units 10.0 units 7.8 units 7.8 units 7.2 units 7.2 units Skip to navigation page 1 of 1

Answer 1

To find the distance between the points (9, 2) and (3, 6) on the coordinate plane, you can use the distance formula:

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

Where $(x_1,y_1)$ are the coordinates of the first point and $(x_2,y_2)$ are the coordinates of the second point.

For the points (9, 2) and (3, 6):

• $x_1=9$, $y_1=2$
• $x_2=3$, $y_2=6$

Now, plug these values into the formula:

$$d=\sqrt{(3-9{)}^2+(6-2{)}^2}$$ $$d=\sqrt{(-6{)}^2+(4{)}^2}$$ $$d=\sqrt{36+16}$$ $$d=\sqrt{52}$$

To simplify $\sqrt{52}$:

$$\sqrt{52}=\sqrt{4\times 13}=2\sqrt{13}$$

Now, calculating the approximate value of $d$:

$$\sqrt{13}\approx 3.605551275$$ $$d\approx 2\times 3.605551275\approx 7.21110255$$

Rounding to the nearest tenth:

$$d\approx 7.2\text{ units}$$

Thus, the distance between the two points, rounded to the nearest tenth of a unit, is $7.2$ units.