Question

7
which of the following steps were applied to △abc obtain △abc ?

a. shifted 3 units right and 2 units up
b. shifted 2 units right and 3 units up
c. shifted 3 units right and 3 units up
d. shifted 4 units right and 3 units up

Explanation:

Step1: Identify coordinates of a point

Take point \( A \) from \( \triangle ABC \). Let's assume \( A \) has coordinates \( (2, 5) \) (from the graph). Point \( A' \) in \( \triangle A'B'C' \) has coordinates \( (5, 7) \)? Wait, no, let's check again. Wait, maybe better to take \( A \): looking at the grid, \( A \) is at \( (2, 5) \)? Wait, no, let's see the x-axis: the grid lines. Let's take point \( A \): x-coordinate is 2, y-coordinate is 5? Wait, \( A' \) is at x=5, y=7? Wait, no, maybe \( A \) is at (2, 5) and \( A' \) is at (5, 7)? Wait, no, let's check the shift. Wait, maybe take point \( A \): let's find its coordinates. From the graph, \( A \) is at (2, 5)? Wait, no, the x-axis: the first grid after 0 is 2? Wait, no, the x-axis has marks at -8, -4, -2, 0, 2, 4, 6, 8, 10. So each grid square is 1 unit. So point \( A \): x=2, y=5? Wait, \( A' \) is at x=5, y=7? Wait, no, maybe \( A \) is at (2, 5) and \( A' \) is at (5, 7)? Wait, the difference in x: 5 - 2 = 3, difference in y: 7 - 5 = 2? No, that's not matching. Wait, maybe I made a mistake. Let's take point \( B \). \( B \) is at (3, 10)? Wait, no, \( B \) is at (3, 10)? Wait, \( B' \) is at (6, 12)? Wait, 6 - 3 = 3, 12 - 10 = 2. No, that's not. Wait, maybe point \( A \) is at (2, 5), \( A' \) is at (5, 7)? No, 5-2=3, 7-5=2. But option A is 3 right and 2 up. Wait, but let's check again. Wait, maybe \( A \) is at (2, 5), \( A' \) is at (5, 7)? Wait, 5-2=3 (right), 7-5=2 (up). So that's 3 right and 2 up. But let's check another point. \( C \): \( C \) is at (6, 5)? Wait, \( C' \) is at (9, 7)? 9-6=3, 7-5=2. So yes, 3 units right and 2 units up. Wait, but option A is "Shifted 3 units right and 2 units up". Wait, but let's check the options. Option A: 3 right, 2 up. Option B: 2 right, 3 up. Option C: 3 right, 3 up. Option D: 4 right, 3 up. Wait, maybe I messed up the coordinates. Let's take point \( A \): from the graph, \( A \) is at (2, 5), \( A' \) is at (5, 7). So x-shift: 5 - 2 = 3, y-shift: 7 - 5 = 2. So that's 3 units right and 2 units up. So option A. Wait, but let's confirm with another point. \( B \): \( B \) is at (3, 10), \( B' \) is at (6, 12). 6 - 3 = 3, 12 - 10 = 2. So same shift. \( C \): \( C \) is at (6, 5), \( C' \) is at (9, 7). 9 - 6 = 3, 7 - 5 = 2. So yes, 3 units right and 2 units up. So the correct option is A.

Wait, but maybe I made a mistake in coordinates. Let's re-examine. The x-axis: each grid is 1 unit. So point \( A \): x=2, y=5. \( A' \): x=5, y=7. So 5-2=3 (right), 7-5=2 (up). So shift is 3 right and 2 up. So option A.

Step2: Verify with another point

Take point \( C \): \( C \) is at (6, 5), \( C' \) is at (9, 7). \( 9 - 6 = 3 \) (right), \( 7 - 5 = 2 \) (up). Same shift. So the translation is 3 units right and 2 units up, which is option A.

Answer:

A. Shifted 3 units right and 2 units up