Question

Triangle ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of B after both reflections?

A) (7,1)
B) (-7,-1)
C) (-7,1)
D) (7,-1)

https://tisd3080-hs-ccl.gradpoint.com/Resource/9515325,0/Assets/testitemimages/geometry_b/transformations/mc039-1.jpg

Answer 1

Hope this helps as I can not give direct answers.
Across the x-axis
(x, y) → (x, −y)
Across the y-axis
(x, y) → (−x, y)
Across the line y = x
(x, y) → (y, x)
Across a horizontal or vertical line
Count the distance between each point on the figure and the line of reflection. Then, for each point, count this same distance from the line of reflection to find the corresponding point.
Remember that a reflection can also be seen as a function, which is a type of input/output machine. If you had a point at (2, 3) and wanted to reflect it using the rule (x,y) → (−x,y), you could place 2 in for x, and you would get −2 for your x-coordinate since the rule says to take the opposite of the x-coordinate. If we place 3 in for y and follow the rule, our output is 3 since the y-coordinate remains unchanged. Our new coordinate would be (−2, 3).