On a dot grid, the left half of a symmetric figure is a rectangle with vertices at A(2, 1), B(2, 4), C(5, 4), and D(5, 1). The line of symmetry is the vertical line x = 5. Ravi reflects the left half to complete the symmetric figure. What is the total area of the completed symmetric figure in square units?
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Worked Solution
Step 1: Identify the dimensions of the left half.
Width: x = 2 to x = 5 → width = 5 - 2 = 3 units.
Height: y = 1 to y = 4 → height = 4 - 1 = 3 units.
Step 2: Area of left half = 3 x 3 = 9 square units.
Step 3: Reflect across x = 5.
A(2,1) maps to A'(8,1) since 2 x 5 - 2 = 8.
B(2,4) maps to B'(8,4).
C(5,4) and D(5,1) lie on the mirror and stay.
Step 4: Completed figure spans x = 2 to x = 8 (width = 6), y = 1 to y = 4 (height = 3).
Step 5: Total area = 6 x 3 = 18 square units.
Answer: 18 square units.
Correct answer: 18 square units
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