Right △ABC has coordinates A(-7, 3), B(-7, 10), and C(-1, 3). The triangle is reflected over the x-axis and then reflected again over the y-axis to create △A'B'C'. Which are the coordinates of vertex A'?
A= (7, -3)
To find the coordinates of vertex A' after reflecting triangle ABC over the x-axis and then over the y-axis, we need to consider the reflections individually.
1. Reflection over the x-axis:
When a point is reflected over the x-axis, its y-coordinate changes sign while the x-coordinate remains the same.
The coordinates of A after reflecting over the x-axis will be (-7, -3).
2. Reflection over the y-axis:
When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same.
The coordinates of A' after reflecting over the y-axis will be (7, -3).
Therefore, the coordinates of vertex A' in triangle A'B'C' are (7, -3).
To find the coordinates of vertex A' after reflecting the triangle over the x-axis, we need to change the sign of the y-coordinate of A.
The y-coordinate of A is 3. When we reflect it over the x-axis, the sign changes, giving us -3. So, the new y-coordinate of A' is -3.
The x-coordinate of A remains the same, which is -7.
Therefore, the coordinates of vertex A' are (-7, -3).
Making a sketch will certainly help you to understand the question
I will use point B(-7,10) to illustrate
reflection over the x-axis: (-7,10) ----> (-7,-10)
reflection of this new point over the y-axis: (-7,-10) ----> (7,-10)
So in effect the two transformation have resulted in a reflection in the origin, that is
(x,y) ----> (-x,-y) , (the signs have reversed)
Now apply this to point A.