Enter your answer and show all the steps that you use to solve this problem in the space provided.
The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "➡" For example: P(0, 0) ➡"P′(1, 2).
Triangle ABC has coordinates A(1,4); B(3,-2); and C(4,2). Find the coordinates of the image
A,B,C after a reflection over the x-axis.
such a reflection takes (x,y)➡(x,-y)
so just flip all the signs of the y-values
To find the coordinates of the image A', B', C' after a reflection over the x-axis, we need to change the y-coordinate of each point while keeping the x-coordinate the same.
Here are the steps to solve this problem:
Step 1: Write down the given coordinates of each point:
A(1,4), B(3,-2), and C(4,2).
Step 2: To reflect a point over the x-axis, we change the sign of the y-coordinate without modifying the x-coordinate.
For point A(1,4), the x-coordinate remains 1, but the y-coordinate changes sign, becoming -4. So the image of point A is A'(1,-4).
For point B(3,-2), the x-coordinate remains 3, but the y-coordinate changes sign, becoming 2. So the image of point B is B'(3,2).
For point C(4,2), the x-coordinate remains 4, but the y-coordinate changes sign, becoming -2. So the image of point C is C'(4,-2).
Step 3: Write down the coordinates of the image points:
The coordinates of the image A' are A'(1,-4), of B' are B'(3,2), and of C' are C'(4,-2).
Therefore, the coordinates of the image of triangle ABC after a reflection over the x-axis are:
A'(1,-4), B'(3,2), and C'(4,-2).