Question

1. Reflect triangle A across the line x = 2.

Answer 1

Answer:

Rule:  Reflect the figure across the y-axis then translate the reflected figure 4 units to the right.

Step-by-step explanation:

Part 1

Points of Figure A:

(2, 2)

(8, 4)

(6, 8)

Draw a line at x = 2, then reflect each point across the line

(2, 2) → (2, 2)

(8, 4) → (-4, 4)

(6, 8) → (-2, 8)

Part 2

Reflection in the y-axis:  (x, y) → (-x, y)

As the y-values of our two figures have not changed, the first part of the rule is: reflect across the y-axis

If we reflect the figure across the y-axis, the points of the reflected figure are:

(-2, 2)

(-8, 4)

(-6, 8)

To bring the reflected figure back to where we want it (reflection in x = 2) we need to translate the figure 4 units to the right:

(-2 + 4, 2) = (2, 2)

(-8 + 4, 4) = (-4, 2)

(-6 + 4, 8) = (-2, 8)

So the final rule is:

Reflect the figure across the y-axis then translate the reflected figure 4 units to the right.

Answer 2

Draw a perpendicular at x=2

Now reflect each coordinates across there

(2,2)

• Will remain same as x=2 is on Q1 positive side

(8,4)

• x coordinate=2-8=-6
• y coordinate=4(same)

New coordinate (-6,4)

(6,8)

• x coordinate=2-6=-4
• y coordinate is same

New coordinate

• (-4,8)