Answer:
- The coordinates of A' are (4x, 4y).
- The coordinates of B' are (4p, 4q).
- The coordinates of A are (x, y).
- The coordinates of B are (p, q).
Explanation:
When a triangle is enlarged with a scale factor of 4 and the center of enlargement is (0,0), the coordinates of the vertices A' and B' can be found by multiplying the coordinates of the original vertices A and B by the scale factor.
Let's assume the original coordinates of A are (x, y).
To find the coordinates of A', we multiply each coordinate by the scale factor of 4:
A' = (4x, 4y)
Similarly, let's assume the original coordinates of B are (p, q).
To find the coordinates of B', we multiply each coordinate by the scale factor of 4:
B' = (4p, 4q)
Now, to find the coordinates of A and B, we need to reverse the enlargement by dividing the coordinates of A' and B' by the scale factor.
For A:
x = (4x) / 4 = x
y = (4y) / 4 = y
So, the coordinates of A are (x, y).
For B:
p = (4p) / 4 = p
q = (4q) / 4 = q
So, the coordinates of B are (p, q).
To summarize:
- The coordinates of A' are (4x, 4y).
- The coordinates of B' are (4p, 4q).
- The coordinates of A are (x, y).
- The coordinates of B are (p, q).