The coordinates of the vertices of triangle ABC are A (-5,1), B (-2,3) and C (-4,7). The triangle is reflected over the line x=2. What is the sum of the x-coordinates of points A', B' and C'(the points after the reflection)?
The y values will not change,
the new x value will be 2 + (2-oldx)
eg A(-5,1) will become A'(2+(2+5),1) or A'(9,1)
Find B' and C', then add up the x-coordinates.
To reflect a point over a vertical line, we swap the x-coordinate with the line's equation value. In this case, the line of reflection is x=2.
Let's find the coordinates of each reflected point:
For Point A, the x-coordinate is -5. When reflected over the line x=2, we swap the x-coordinate with 2:
A' = (2, 1)
For Point B, the x-coordinate is -2. When reflected over the line x=2, we swap the x-coordinate with 2:
B' = (4, 3)
For Point C, the x-coordinate is -4. When reflected over the line x=2, we swap the x-coordinate with 2:
C' = (6, 7)
Now, let's calculate the sum of the x-coordinates of A', B', and C':
Sum = 2 + 4 + 6 = 12
Therefore, the sum of the x-coordinates of points A', B', and C' is 12.