A triangle has points A(2, 2), B(2, 4), and C(6, 3) and is reflected over the x-axis. A'B'C' are the coordinates of the reflected image. What is the B' coordinate
since reflection over the x-axis takes (x,y) -> (x,-y)
just change the sign of the y-coordinate for each point.
To find the coordinates of the reflected image of a triangle over the x-axis, we need to reflect each individual point over the x-axis.
First, let's understand how to reflect a point over the x-axis. When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate changes its sign. For example, the point (x, y) becomes (x, -y) after reflecting over the x-axis.
Now, let's reflect each point of the original triangle over the x-axis.
Point A(2, 2): After reflecting A over the x-axis, the y-coordinate changes its sign. So, A'(2, -2).
Point B(2, 4): After reflecting B over the x-axis, the y-coordinate changes its sign. So, B'(2, -4).
Point C(6, 3): After reflecting C over the x-axis, the y-coordinate changes its sign. So, C'(6, -3).
We are looking for the coordinate of B'. As we found earlier, B' has the same x-coordinate as B but a different sign for the y-coordinate. Therefore, the coordinate of B' is (2, -4).
So, the B' coordinate after reflecting the triangle A'B'C' over the x-axis is (2, -4).