Review for Unit 2 Learning Check Point 1: Distance Formula, Midpoint Formula, Translation, Rotation, Reflection

Review for Unit 2 Learning Check Point 1

by Matthew Lopez

​Overview

​This week you will be taking the Unit 2 Learning Check Point #1. The skills involved will include:

• ​Distance Formula

• ​​Midpoint Formula

• ​Rotation, Reflection, Translation

​The next 3 slides are notes on the Distance Formula

​

​Write down the:

• ​Distance Equation

• ​The reminder about Squaring vs Square Rooting

• ​Entire example problem

​

​

​Distance Formula Example (Write it down)

​What is the distance

between (1,2) and (-3,-5)?

​

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

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

Find the distance between (-12, 1) and (12, -1).

• 24.05
• 24.06
• 24.07
• 24.08

Multiple Choice

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

• 8.9
• 9.8
• 10.3
• 11

Multiple Choice

Find the distance.

• 9.7
• 10.7
• 11.7
• 12.7

​Midpoint Formula

​The midpoint formula finds the point perfectly between two other points.

​

The point perfectly in the middle is called the midpoint.

​Mid Point Formula Example

Multiple Choice

Find the midpoint of the line segment with endpoints (-2,0) & (9,-1).

• (1, 3)

• (3.5, -.5)

• (-.5, 3.5)

• (6, -.5)

Multiple Choice

(2, -11)  (-9, 0)

• (2, 9)
• (3.5, -5.5)
• (-3.5, -5.5)

Multiple Choice

(8, -9)  (0, 5)

• (-2, 4)
• (2, 4)
• (4, -2)

Multiple Choice

(14, 0)  (-7, 5)

• (3, 2)
• (3.5, 2.5)
• (2,3)

​Translations Explained

​A translation is just a slide up, down, left or right.

​

​For example if I say I am (x+2, y+2), it means I am moving a point two right because x+2 means going right two, and moving the point up 2 because y+2 means going up two.

​

​

​Example Part 1

​Example Part 2

Multiple Choice

Determine where X' would be if you translated X 3 units to the left and 9 units down.

• (-4, 4)
• (-10, 2)
• (-4, -5)
• (-1, 5)

Multiple Choice

How is Quadrilateral EFGH translated to E'F'G'H'?

• 6 down
• 6 down, 1 right
• 6 down, 3 left
• 8 down, 1 right

Multiple Choice

How is triangle ABC being translated to triangle A'B'C'?

• up 3, left 8
• up 9, left 4
• down 3, right 8
• down 9, right 4

​Rotation Explained

​Rotation is a movement that keeps the figure looking EXACTLY the same, except it has been turned around a point and moved a certain amount.

​

​Watch a bunch of GIFs to help explain it: https://www.mathsisfun.com/geometry/rotation.html

​Reflection Explained

​Reflections Explained Continued

​Major Take aways:

• ​A reflection is the same distance from the line of reflection (or mirror line) as the original.

• ​The figures are identical (congruent) except they are flipped over the line. (Same size same shape)

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• Reflection across the line y= -x

• Reflection across the line y=x

• Reflection across the y-axis

• Reflection across the x-axis

Multiple Choice

Is the picture being reflected in the y-axis or x-axis?

• y-axis
• x-axis

Multiple Choice

The NEW figure created from a transformation is...

• Congruent

• Preimage

• Image

• Angle

Multiple Choice

Congruent geometric figures have the:

• Same size
• Sides Equal
• Same Size and Same Shape
• Angles Equal

Multiple Choice

The picture represents what kind of transformation?

• Translation

• Reflection

Multiple Choice

State the line of reflection.

• Reflection across y-axis
• Reflection across x-axis
• Reflection across x = 1
• Reflection across y = 1