Introduction to Distance and Midpoint Formulas

​Distance Formula

&

Midpoint Formula​

Distance Formula

​

Some text here about the topic of discussion

Multiple Choice

Between any two points, it is the length of the line segment joining the points.

• Length

• Distance

• Line

• Segment

Multiple Choice

The x-axis is _______?

• vertical
• diagonal
• criss-cross
• horizontal

Multiple Choice

The y-axis is _______?

• Vertical
• Horizontal
• criss-cross
• diagonal

Multiple Choice

The distance formula is another way to write which of the following?

• quadratic formula

• slope formula

• Pythagorean theorem

• none of these answers

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

A(2,0) B(-2,4) is written as

• $$d\ =\ \sqrt{\left(4-2\right)^2\ -\ \left(0-2\right)^2}$$

• $$d\ =\ \sqrt{\left(4-0\right)^2\ -\ \left(-2-2\right)^2}$$

• $$d\ =\ \sqrt{\left(-2\ +0\right)^2\ +\ \left(4+2\right)^2}$$

• $$d\ =\ \sqrt{\left(-2-2\right)^2\ +\ \left(4-0\right)^2}$$

Multiple Choice

What is the distance between AB

• 0

• 8

• 9

• 7

Multiple Choice

What is the distance between AB?

• 0

• undefined

• 5

• 4

Multiple Choice

How is AB written in the distance formula?

• $$d\ =\ \sqrt{\left(5-3\right)^2\ +\ \left(0--2\right)^2}$$

• $$d\ =\ \sqrt{\left(2-5\right)^2\ +\ \left(3\ -0\right)^2}$$

• $$d\ =\ \sqrt{\left(5-3\right)^2\ -\ \left(0--2\right)^2}$$

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

Multiple Choice

What is coordinate X?

• (2,5)

• (4,4)

• (4,3)

• (1,0)

Multiple Choice

Using the Distance Formula what is the distance between

(3,4) (7,9)

• $$41$$  

• $$\sqrt[]{38}$$  

• $$\sqrt[]{41}$$  

• $$\sqrt[]{25}$$  

Multiple Choice

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

• 8.9
• 9.8
• 10.3
• 11

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 (-4, 5) and (7, 18).

• 15.96
• 16.08
• 16.23
• 17.03

Multiple Choice

What is the distance between the two points?

• 6.3
• 6.5
• 6.7
• 16

Multiple Choice

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

• 15
• 17
• 4.12
• 3.87

​Midpoint Formula

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

Multiple Choice

What is the midpoint between (3, -1) and (7, -5)

• (5, -2)
• (10, -6)
• (5, -3)
• (2, -2)

Multiple Choice

Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)

• (-1, 13)
• (13, 1)
• (13, -1)
• (5, 13)

Multiple Choice

What is the midpoint between (-4,4) and (-2,2)?

• (3,2)
• (-3,3)
• (4,5)
• (6,7)

Multiple Choice

The point that divides the given line segment into two equal parts; the point that bisects the line.

• Midpoint

• Distance

• Center

• Line Segment

Multiple Choice

Find the midpoint of the line segment with the given endpoints.

(-4,4) and (-2,2)

• $$M=\left(3,3\right)$$  

• $$M=\left(-3,-3\right)$$  

• $$M=\left(-3,3\right)$$  

• $$M=\left(3,-3\right)$$  

Multiple Choice

Find the midpoint of the line segment with the given endpoints.

(-1,1) and (5,-5)

• $$M=\left(-2,2\right)$$  

• $$M=\left(2,-2\right)$$  

• $$M=\left(-2,-2\right)$$  

• $$M=\left(2,2\right)$$  

Multiple Choice

Find the midpoint of the line segment with the given endpoints.

(2,-1) and (-6,0)

• $$M=\left(-2,-\frac{1}{2}\right)$$  

• $$M=\left(2,\frac{1}{2}\right)$$  

• $$M=\left(-\frac{1}{2},-2\right)$$  

• $$M=\left(\frac{1}{2},2\right)$$  

Multiple Choice

Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)

• (-1, 13)
• (13, 1)
• (13, -1)
• (5, 13)

Multiple Choice

What is the center of MN given M(3, -1) and N(7, -5)

• (5, -2)
• (10, -6)
• (5, -3)
• (2, -2)

Multiple Choice

What point is halfway between (3, -1) and (8, -6)?

• (11, -7)
• (-5.5, -3.5)
• (5.5, -3.5)
• (2, -2)

Finding the Missing Endpoint

Multiple Choice

The middle of a line is called the _______________.

• endpoint

• midpoint

• slope

• distance

Multiple Choice

  Find the missing endpoint if the midpoint is at (2, -5) and one endpoint is at (12, -5).

• (2, -5)
• (10, -8)
• (-8, -5)
• (12, -5)

Multiple Choice

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,8)   Midpoint (0,9)

• (-9, 10)
• (1.5, -1)
• (4.5, -0.5)
• (8.5, 4.5)

Multiple Choice

Point M with coordinates (3,4) is the midpoint of the line AB and A has the point (-1,6). What is the point of B?

• (1,5)
• (2,10)
• (7,2)
• (1,2)

Multiple Choice

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(5, -6) and M(4,3).

• (3, 12)

• (6, 4)

• (1, 2)

Multiple Choice

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(-3, 7) and M(-2,5).

• (6, 8)

• (-1, 3)

• (2, -4)

Multiple Choice

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(-2, 9) and M(8, 0).

• (-6, 0)

• ( 6, 9)

• (18, -9)

Multiple Choice

Plot the points A = (-1, 8) and M = (2, 3) in the xy-plane. If M is the midpoint of a line segment AB, find the coordinates of B.

• (5,-2)

• (-5,2)

• (6, 2)

• (-1,4)