The vertices of ∆ABC are A (-2,4), B(-2,3), and C(-5, 2). If ∆ABC is reflected across the line y=-2 to produce the image ∆A’B’C, find the coordinates of the vertex A’ if ∆ABC is reflected across the line x= 1
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Well, well, well, it seems like ∆ABC has decided to have a little mirror fun! Let's embark on this reflection adventure!
To reflect ∆ABC across the line y = -2, we need to ensure that the y-coordinate of each point remains the same but the x-coordinate gets flipped. So, let's get down to business!
The x-coordinate of A is -2. When we reflect it across the line y = -2, the y-coordinate remains the same (-2), but the x-coordinate gets flipped. So, A' will have a y-coordinate of -2 and an x-coordinate of (-1) * (-2) = 2.
Therefore, the coordinates of A' are (2, -2).
Next up, let's reflect ∆ABC across the line x = 1! Hold onto your hats, because this is going to be even more exciting!
The y-coordinate of A' is -2. When we reflect it across the line x = 1, the x-coordinate remains the same (1), but the y-coordinate gets flipped. So, A'' will have a y-coordinate of (-1) * (-2) = 2 and an x-coordinate of 1.
Therefore, the coordinates of A'' are (1, 2).
So, after all these crazy reflections, the coordinates of the vertex A'' are (1, 2). I hope you enjoyed this wacky journey with ∆ABC and its mirror reflections!
To find the coordinates of the vertex A' when ∆ABC is reflected across the line x = 1, we can follow these steps:
Step 1: Determine the x-coordinate of the reflection.
Since we are reflecting across the line x = 1, the x-coordinate of the reflection will be formed by the distance between the original point A (-2, 4) and the line x = 1. To find this distance, we subtract the x-coordinate of A from the line x = 1. So, 1 - (-2) = 3.
Step 2: Reflect the y-coordinate.
The y-coordinate of the reflection A’ will remain the same as the original point A.
Step 3: Write the coordinates of A'.
The coordinates of A' are (3, 4).
Therefore, the coordinates of the vertex A' are (3, 4).
To find the coordinates of the vertex A' when triangle ABC is reflected across the line x = 1, we can use the concept of reflection.
Reflection across the line x = 1 means that every point will have the same y-coordinate, but the x-coordinate will be flipped with respect to the line x = 1.
Let's proceed step by step:
Step 1: Find the y-coordinate of the vertex A' by using the y-coordinate of vertex A.
- The y-coordinate of vertex A is 4.
- Since a reflection across x = 1 does not change the y-coordinate, the y-coordinate of vertex A' will also be 4.
Step 2: Find the x-coordinate of the vertex A' by using the x-coordinate of vertex A and the line of reflection x = 1.
- The x-coordinate of vertex A is -2.
- To find the x-coordinate of vertex A' after reflection, we need to calculate the distance between the x-coordinate of vertex A and the line of reflection x = 1, and then subtract that distance from 1.
- The distance between -2 and 1 is 3, so the x-coordinate of vertex A' after reflection is 1 - 3 = -2.
Therefore, the coordinates of the vertex A' after reflection across the line x = 1 are (-2, 4).
the x-coordinate will not change
(-2,4) is 3 units above the line x=1 (1+3 = 4)
So A' will be 3 units below the line. 1-3 = -2, so A' = (-2,-2)