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### Course: High school geometry>Unit 1

Lesson 5: Reflections

Sal is given two line segments on the coordinate plane, and determines the reflection that maps one of them into the other.

## Want to join the conversation?

• I have a test in a few weeks and I like to check my work over and over again, So, is there any other way to do it so I can check if the answers from all the strategies to see if they match?
• Not that I know of, but like Sal did at , you can draw the line across and measure the units on either side of the line of reflection. They should come out equally if you are correct. Just be sure to draw the line correctly though!
• How does this guy have such good handwriting?
• Every time he says similarly incorrectly he writes a random number from 1 - 10
• How would i reflect a point if it told me to reflect about the given line of y=1/2x + 16
• To reflect a point across a given line, you can use the following steps:

Find the slope of the given line.
Determine the negative reciprocal of the slope. This will be the slope of the perpendicular line.
Use the perpendicular slope and the given line's equation to find the equation of the perpendicular bisector. This bisector is the line about which the reflection occurs.
Find the intersection point of the given line and the perpendicular bisector. This point is the center of reflection.
Use the center of reflection to calculate the distance between the given point and the center.
Reflect the point across the center using the distance and direction.
Let's go through an example:

Suppose you have a point P(x, y) and the line

=
1
2

+
16
y=
2
1

x+16 is the line of reflection.

The slope of the given line is
1
/
2
1/2.

The negative reciprocal of
1
/
2
1/2 is

2
−2, so the slope of the perpendicular bisector is

2
−2.

Use the point-slope form to find the equation of the perpendicular bisector. Let's say the point P is
(

0
,

0
)
(x
0

,y
0

):

0
=

2
(

0
)
y−y
0

=−2(x−x
0

)

Find the intersection point of

=
1
2

+
16
y=
2
1

x+16 and the perpendicular bisector. This point is the center of reflection.

Calculate the distance between the given point P and the center of reflection.

Reflect the point across the center using the distance and direction.
• Is there a faster way to find a point (-5, 1) with a line of reflection of y = -3 without graphing it?
• Yes there is! All you have to do is try to imagine the points in your head and the line you're reflecting on. Also make sure you have good knowledge of each quadrant on the coordinate plane.

Oh and sorry I'm 7 years late
• Who knew numbers were vain enough to use mirrors...
• What does it mean when a line intersects?
(1 vote)
• When a line intersects, two lines cross each other. An example is a perpendicular line. Two lines intersect creating a 90 degree angle.
• At how did you know that it was over 2? Like how did you get that?
• Hi Hailey!
Sal is taking the average of the x coordinates and the average of the y coordinates. To calculate a non-weighted average, you add the appropriate numbers together and divide by how many different numbers you have. So if I wanted the average of the set {2, 3, 4, 5} you would do it this way:
2 + 3 + 4 +5 = 14
There are 4 addends (numbers that are being added together) here, so we will divide 14 by 4.
14/4 = 3.5
Therefore, the average {2, 3, 4, 5} is 3.5.
Here the 2 x coordinates are -4 and 2, and the y coordinates are -4 and -6.
Sal adds -4 + 2 = -2, -2 / 2 = -1.
-4 + -6 = -10, -10 / 2 = -5.
These are the coordinates of one endpoint of the line of reflection.
I hope this helped you!
Have a great day!