Question

Consider triangle ABC with A (3,2), B(2,6), and C(5,4). Find the coordinates of the image of triangle ABC when triangle ABC is reflected about the line x = -2.

A. A'(-7,2), B'(-6,6), C'(-9,4)
B. A'(-3,2), B'(-2,6), C'(-5,4)
C. A'(-5,2), B'(-4,6), C'(-7,4)
D. A'(-2,2), B'(-3,6), C'(-6,4)

Answer 1

The coordinates of the reflected points are found by measuring the horizontal distance from each point's x-coordinate to the line of reflection (x = -2) and then placing the image point the same distance on the opposite side of this line, while keeping the y-coordinate the same. The reflected coordinates for triangle ABC are A'(-7,2), B'(-6,6), C'(-9,4).

Step-by-step explanation:

To determine the coordinates of the image of triangle ABC when it is reflected about the line x = -2, we must consider how reflections work on the Cartesian plane. A reflection across a vertical line like x = -2 means that the x-coordinate of each point in the triangle will change symmetrically across this line. Specifically, the distance from each original x-coordinate to the line of reflection will be the same as from the new x-coordinate to the line of reflection, but on the opposite side.

Here's the process step by step for point A (3,2):

1. Determine the distance of point A's x-coordinate from the line of reflection: it is 3 - (-2) = 5 units to the right.
2. To reflect point A over the line x = -2, we move A the same distance to the left of the line, which will be at -2 - 5 = -7.
3. The y-coordinate remains the same after the reflection since the line of reflection is vertical. So, point A after reflection is A'(-7,2).

Repeating these steps for points B and C:

• Point B: The original distance from the line of reflection is 2 - (-2) = 4 units to the right. So after reflection, we get B'(-6,6).
• Point C: The original distance from the line of reflection is 5 - (-2) = 7 units to the right. So after reflection, we get C'(-9,4).

Therefore, the correct answer is A'(-7,2), B'(-6,6), C'(-9,4), which corresponds with option A.