A triangle with vertices A(–3, 4), B(3, 1),and C(–1, –5) is translated 5 units left and 3 units up. Find the coordinates of A', B', and C'.
To translate a point by a given number of units left or right, and up or down, we simply add or subtract the respective values from the coordinates of the original point.
Given:
Point A: (-3, 4)
Point B: (3, 1)
Point C: (-1, -5)
Translation:
Left: 5 units
Up: 3 units
To find the new coordinates:
For point A':
1. Subtract 5 from the x-coordinate of A (-3 - 5 = -8)
2. Add 3 to the y-coordinate of A (4 + 3 = 7)
So, point A' is (-8, 7)
For point B':
1. Subtract 5 from the x-coordinate of B (3 - 5 = -2)
2. Add 3 to the y-coordinate of B (1 + 3 = 4)
So, point B' is (-2, 4)
For point C':
1. Subtract 5 from the x-coordinate of C (-1 - 5 = -6)
2. Add 3 to the y-coordinate of C (-5 + 3 = -2)
So, point C' is (-6, -2)
Therefore, the coordinates of A', B', and C' are (-8, 7), (-2, 4), and (-6, -2) respectively.
To find the new coordinates of each vertex after the translation, we need to apply the translation vector to each point.
The translation vector (5 units left, 3 units up) tells us that for each point, we need to subtract 5 from the x-coordinate and add 3 to the y-coordinate.
Let's find the new coordinates for each vertex:
For vertex A:
Original coordinates: A(-3, 4)
Translation: (-5, 3)
New coordinates:
A' = (x - 5, y + 3)
A' = (-3 - 5, 4 + 3)
A' = (-8, 7)
For vertex B:
Original coordinates: B(3, 1)
Translation: (-5, 3)
New coordinates:
B' = (x - 5, y + 3)
B' = (3 - 5, 1 + 3)
B' = (-2, 4)
For vertex C:
Original coordinates: C(-1, -5)
Translation: (-5, 3)
New coordinates:
C' = (x - 5, y + 3)
C' = (-1 - 5, -5 + 3)
C' = (-6, -2)
Therefore, the coordinates of the translated triangle are:
A'(-8, 7), B'(-2, 4), and C'(-6, -2).