Pythagorean Theorem and Distance Formula

Distance Formula

Review and Practice

Multiple Choice

Which of the following represents the Distance Formula?

• $$a^2\ +\ b^2\ =\ c^2$$

• $$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }-\ y_1\right)^2}$$

Multiple Select

Which of the following shows the correct way to insert the following coordinates into the DIstance Formula?

(3, 4) , (7, 1)

• $$d\ =\ \sqrt{\left(4\ -\ 3\right)^2\ +\ \left(7\ -\ 1\right)2}$$

• $$d\ =\ \sqrt{\left(7\ -\ 3\right)^2\ +\ \left(1\ -\ 4\right)^2}$$

• $$d\ =\ \sqrt{\left(7\ -\ 4\right)^2\ +\ \left(1\ -\ 3\right)^2}$$

• $$d\ =\ \sqrt{\left(3\ -\ 7\right)^2\ +\ \left(4\ -\ 1\right)^2}$$

• $$d\ =\ \sqrt{\left(3\ +\ 7\right)^2\ -\ \left(4\ +\ 1\right)^2}$$

Multiple Choice

Find the distance between the points (5, 7) and (-2, -2).

• 5.7

• 5.8

• 8.6

• 11.4

Multiple Choice

What is the distance between (-3, 2) and (5, -1)

• 11

• 8.5

• 1.7

• 7.3

Multiple Choice

Find the distance between (0, 10) and (12, 1).

• 12

• 11

• 15

• 16

Pythagorean Theorem Review

Multiple Choice

One end of a cable is attached to the top of a flag pole and the other end is attached 6 feet away from the base of the pole. The height of the flagpole is 12 feet. What is length of the cable?

• 13.4 ft

• 13.1 ft

• 6 ft

• 10.4 ft

Multiple Choice

Rectangle JKLM is shown. To the nearest tenth, what is the distance from J to L?

• 5.0 cm

• 10.2 cm

• 15.3 cm

• 21.0 cm

Multiple Choice

If a triangle has sides 13, 17, and 27 is it right, acute or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

Is a triangle with sides 21, 24 and 28 right, acute or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

Is a triangle with sides 7, 24, and 25 right, acute, or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

To the nearest tenth, find the hypotenuse of a right triangle with legs 12.1 and 16.2.

• 408.9

• 116.0

• 20.2

• 10.8

Multiple Choice

If a triangle has sides 13, 17, and 27 is it right, acute or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

How is the distance formula correctly written:

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$$

• $$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)^2}$$

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$$

• d = $$\sqrt{\left(x\right)^2-\ \left(y\right)^2}$$

Multiple Choice

A(3,1) B(-2,-1) written correctly is:

• $$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$$

• $$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$$

• $$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

• $$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

Multiple Choice

The distance between point K: (1,2) and Point L: (9,5) written correctly is:

• $$\sqrt{\left(9-5\right)^2\ +\ \left(2-1\right)^2}$$

• $$\sqrt{\left(9-1\right)^2\ +\ \left(5-2\right)^2}$$

• $$\sqrt{\left(9-5\right)^2\ -\ \left(2-1\right)^2}$$

• $$\sqrt{\left(9-2\right)^2\ -\ \left(5-1\right)^2}$$

Multiple Choice

Simplify

• 9
• √9
• 3√9
• can't simplify

Multiple Choice

What is the distance between (2,9) and (1,5)?

• 15
• 17
• 4.12
• 3.87

Multiple Choice

Find the distance between (3, 24) and (7, 56).

• 32.1
• 32.2
• 32.3
• 32.4

Multiple Choice

Find the distance between (-5, -8) and (-1, -16).

• 8.9
• 9.8
• 10.3
• 11

Multiple Choice

Find the distance between J and K.

• 8.2
• 7.7
• 9
• 10.2

Multiple Choice

Find the distance.

• 9.7
• 10.7
• 11.7
• 12.7