Given points J (1,4), A (3,5), and R(2,1), graph JAR and its reflection image across each line
`1) the x-axis
2) the y-axis
3) y = 2
I need help finding what to graph!
To graph JAR and its reflection image across different lines, you need to follow these steps:
1) Plot the given points J(1,4), A(3,5), and R(2,1) on a coordinate plane.
2) To reflect a point across the x-axis, you keep the x-coordinate the same and change the sign of the y-coordinate. So, to find the reflection image of JAR across the x-axis, you simply change the sign of the y-coordinate of each point. For example, J(1,4) reflects to J'(1,-4), A(3,5) reflects to A'(3,-5), and R(2,1) reflects to R'(2,-1). Now, plot these reflected points.
3) To reflect a point across the y-axis, you keep the y-coordinate the same and change the sign of the x-coordinate. So, to find the reflection image of JAR across the y-axis, you simply change the sign of the x-coordinate of each point. For example, J(1,4) reflects to J'(-1,4), A(3,5) reflects to A'(-3,5), and R(2,1) reflects to R'(-2,1). Plot these reflected points.
4) To reflect a point across a line y = c, you use the formula:
Reflected point (x', y') = (x, 2c - y)
For example, for the line y = 2, the reflection image of JAR can be found by substituting the y-value as 2 in the formula. So, we have:
J'(1,4) reflects to J'(1, 2(2) - 4) = J'(1,0)
A'(3,5) reflects to A'(3, 2(2) - 5) = A'(3,-1)
R'(2,1) reflects to R'(2, 2(2) - 1) = R'(2,3)
Plot these reflected points.
Now, connect the points JAR and J'A'R' to graph JAR and its reflection image across each line.