Given points J(3,3), A(5,5), and R(4,2), graph JAR and its reflection image across the given line.
x=1
To graph the reflection image of JAR across the line x = 1, we need to reflect the points J, A, and R across the line x = 1.
First, let's find the reflection point of J:
Given J(3, 3) and the line x = 1, we can draw a vertical line from J to intersect x = 1. The distance between J and the line x = 1 is 1 unit. So the reflection point of J will be 1 unit to the left of the line x = 1.
Thus, the reflection point of J is J'(0, 3).
Next, let's find the reflection point of A:
Given A(5, 5) and the line x = 1, we can draw a vertical line from A to intersect x = 1. The distance between A and the line x = 1 is 4 units. So the reflection point of A will be 4 units to the left of the line x = 1.
Thus, the reflection point of A is A'(−3, 5).
Finally, let's find the reflection point of R:
Given R(4, 2) and the line x = 1, we can draw a vertical line from R to intersect x = 1. The distance between R and the line x = 1 is 3 units. So the reflection point of R will be 3 units to the left of the line x = 1.
Thus, the reflection point of R is R'(−2, 2).
Now we can graph JAR and its reflection image J'A'R':
- Plot point J(3, 3) and its reflection point J'(0, 3).
- Plot point A(5, 5) and its reflection point A'(−3, 5).
- Plot point R(4, 2) and its reflection point R'(−2, 2).
- Connect points J, A, and R to form the triangle JAR.
- Connect points J', A', and R' to form the triangle J'A'R'.
Here is the graph:
```
|
J' |
(-3, 5) | R' (-2, 2)
-----------|
|
J |
(3, 3) | R (4, 2)
-----------|-------------------
| | | | | | |
-4 -3 -2 -1 1 2 3
```
Triangle JAR is connected by the points J(3, 3), A(5, 5), and R(4, 2). Its reflection image J'A'R' is connected by the points J'(0, 3), A'(-3, 5), and R'(-2, 2).
Note: The line x = 1 is represented by the vertical line passing through x = 1 on the graph.