(7/4) Distance Formula

To find the distance between two points, you can use the Distance Formula, which is similar to using the _________.

• Pythagorean Theorem

• Converse of the Pythagorean Theorem

• Midpoint Formula

• Slope-Intercept Form

Find the distance.

• 7.1

• 7.8

• 8.7

• 8.9

Answer explanation

$d=\sqrt{\left(9-3\right)^2+\left(7-2\right)^2}$

$d=\sqrt{6^2+5^2}=\sqrt{36+25}=\sqrt{61}\approx7.8$

Find the distance.

• 9.7
• 10.7
• 11.7
• 12.7

Tags

CCSS.HSG.GPE.B.7

Find the distance between J and K.

• 8.2
• 7.7
• 9
• 10.2

Tags

CCSS.HSG.GPE.B.7

Becky leaves school to go home. She walks 6 blocks North and then 8 blocks west. How far is Becky from the school?

• 14 blocks

• 12 blocks

• 10 blocks

• 8.5 blocks

Tags

CCSS.8.G.B.8

Use the distance formula to find the distance between the points (1, 5) and (3, 8). Round to one decimal place if necessary.

• 7

• 5.4

• 2.2

• 3.6

Answer explanation

$d=\sqrt{\left(3-1\right)^2+\left(8-5\right)^2}$ $d=\sqrt{2^2+3^2}=\sqrt{4+9}=\sqrt{13}\approx3.6$

Use the distance formula to find the distance between the points (1, 3) and (5, 6) . Round to one decimal place if necessary.

• 3

• 4

• 5

• 6

Use the distance formula to find the distance between the points (2, 9) and (1, 5) . Round to one decimal place if necessary.

• 15

• 17

• 4.12

• 3.87

Use the distance formula to find the distance between (-5, -8) and (-1, -16). Round to one decimal place if necessary.

(a)  

Answer explanation

$d=\sqrt{\left(-1--5\right)^2+\left(-16--8\right)^2}$ $d=\sqrt{\left(-1+5\right)^2+\left(-16+8\right)^2}$ $d=\sqrt{4^2+\left(-8\right)^2}=\sqrt{16+64}=\sqrt{80}\approx8.9$

Use the distance formula to find the distance between the points (4, 3) and (0, 6). Round to one decimal place if necessary.

(a)