Question

Given points A(-5,2), B(-1,5), C(0,3), perform a double reflection over the lines (x=1) followed by (x=3). What are the new coordinates of points A, B, and C after the double reflection?

a. A'(-7,2), B'(-3,5), C'(4,3)
b. A'(-7,2), B'(-3,5), C'(0,3)
c. A'(-5,2), B'(-1,5), C'(0,3)
d. A'(-5,2), B'(-1,5), C'(-4,3)

Answer 1

After performing the double reflections over x=1 and x=3, the new coordinates of points A, B, and C are A'(-7,2), B'(-3,5), and C'(4,3). This corresponds to option a in the choices provided.

Step-by-step explanation:

To find the new coordinates of points A, B, and C after double reflection over the lines x=1 followed by x=3, we will reflect each point across these lines successively.

First reflection over x=1:

• The distance of point A from x=1 is 6 units (to the left). Reflecting it across x=1, we get A" which will be 6 units to the right of x=1, i.e., at x=7. So, A"(7,2).
• For point B, located 2 units left of x=1, after reflection it will be 2 units to the right of x=1, giving us B"(3,5).
• Point C is 1 unit to the left of x=1, after reflection it will be 1 unit to the right, yielding C"(2,3).

Second reflection over x=3:

• Point A"(7,2) is 4 units to the right of x=3. Reflecting across x=3, we get A'(−7,2).
• Point B"(3,5) is coincident with x=3 and will remain unchanged after reflection. Therefore, B'(−3,5).
• Point C"(2,3) is 1 unit to the left of x=3. After reflection, it will be 1 unit to the right, resulting in C'(4,3).

Thus, the new coordinates after the double reflections are A'(-7,2), B'(-3,5), and C'(4,3), which corresponds to option a.