Question

translating figures

triangle abc is translated 6 units to the right and 1 units up.
what are the coordinates of c?
○ c(4, -2)
○ c(4, -0)
○ c(4, 2)
○ c(1, 2)

Explanation:

Step1: Find original coordinates of C

From the graph, original \( C \) has coordinates \( (-2, -3) \) (assuming grid units, x=-2, y=-3).

Step2: Apply translation (right 6, up 1)

For x - coordinate: \( -2 + 6 = 4 \)
For y - coordinate: \( -3 + 1 = -2 \)? Wait, no, maybe I misread. Wait, looking at the options, let's recheck. Wait, maybe original C is (-2, -3)? No, wait the options have (4, -2), (4,0), (4,2), (1,2). Wait, maybe original C is (-2, -3)? Wait no, let's see the grid. Wait, point A is at (-2, -1)? Wait, maybe I made a mistake. Wait, the triangle: B is at (-5, -1), A at (-2, -1), C at (-2, -3). So translating right 6: x: -2 +6=4; up 1: y: -3 +1=-2? But option is C'(4, -2)? Wait no, the options: first option is C'(4, -2)? Wait the options are:

• \( C'(4, -2) \)

• \( C'(4, -0) \) (which is (4,0))

• \( C'(4, 2) \)

• \( C'(1, 2) \)

Wait, maybe original C is (-2, -3)? No, wait maybe I misread the y - axis. Wait, the y - axis: above x - axis is positive, below is negative. Wait, point C: let's count the grid. If A is at (-2, -1), then C is at (-2, -3). Translating right 6: x becomes -2 +6=4. Up 1: y becomes -3 +1=-2. So \( C'(4, -2) \)? But wait the options have \( C'(4, -2) \) as first option. Wait but maybe I made a mistake. Wait, maybe original C is (-2, -3)? Wait no, maybe the original C is (-2, -3), then after translation: x: -2 +6=4, y: -3 +1=-2. So \( C'(4, -2) \). Wait but let's check again.

Wait, maybe the original coordinates of C are (-2, -3). Translating 6 units right: add 6 to x - coordinate: \( -2 + 6 = 4 \). Translating 1 unit up: add 1 to y - coordinate: \( -3 + 1 = -2 \). So \( C'(4, -2) \).

Answer:

\( C'(4, -2) \) (corresponding to the first option: \( C'(4, -2) \))