Question

question 8 of 10 if △abc is reflected across the y-axis, what are the coordinates of a? a. (-1, -3) b. (5, -3)

Explanation:

Answer:

First, we need to determine the original coordinates of point \( A \). From the graph, we can see that point \( A \) has coordinates \( (1, 3) \) (assuming the grid is such that each square is 1 unit). When a point \( (x, y) \) is reflected across the \( y \)-axis, the transformation rule is \( (x, y) \to (-x, y) \).

Applying this rule to point \( A(1, 3) \), we get the coordinates of \( A' \) as \( (-1, 3) \). Wait, but the options given are A. \( (-1, -3) \) and B. \( (5, -3) \). Maybe I misread the coordinates of \( A \). Let's re-examine the graph. Looking at the \( y \)-axis, the \( y \)-coordinate of \( A \): if the horizontal line through \( A \) is at \( y = 3 \)? Wait, maybe the \( y \)-coordinate is 3? Wait, the options have negative \( y \)-coordinates. Wait, maybe the original \( A \) is at \( (1, -3) \)? Wait, the graph: the \( x \)-axis is horizontal, \( y \)-axis vertical. Let's check the grid. The \( y \)-axis: above the \( x \)-axis is positive, below is negative. The point \( A \): let's see the \( x \)-coordinate: from the origin (0,0), moving 1 unit to the right (positive \( x \)), and \( y \)-coordinate: if the line is at \( y = 3 \)? Wait, no, maybe the \( y \)-coordinate is 3? But the options have negative. Wait, maybe I made a mistake. Wait, the options are A. (-1, -3) and B. (5, -3). Wait, maybe the original \( A \) is at \( (1, -3) \)? Let's check the reflection over \( y \)-axis: \( (x, y) \to (-x, y) \). So if \( A \) is \( (1, -3) \), then \( A' \) is \( (-1, -3) \), which is option A.

Wait, maybe the \( y \)-coordinate of \( A \) is -3? Let's look at the graph again. The \( y \)-axis: the numbers below the \( x \)-axis are negative. So if \( A \) is at \( (1, -3) \), then reflecting over \( y \)-axis gives \( (-1, -3) \), which is option A.

So the correct answer is A. (-1, -3)