The coordinates of the vertices of △JKL are J(−2, −3), K(1, −1), and L(4, −2).
The coordinate graph shows triangle J K L with coordinates
* J, negative 2, negative 3,
* K, 1, negative 1.
* L, 4, negative 2.
The triangle is translated 2 units left and 4 units up. What are the coordinates of the vertices of △J′K′L′, the translated triangle?
To translate a point or a shape on a coordinate plane, you simply add or subtract the same value to the x-coordinate and y-coordinate of each vertex.
To translate the triangle 2 units left, subtract 2 from the x-coordinate of each vertex:
J': (-2-2, -3+4) = (-4, 1)
K': (1-2, -1+4) = (-1, 3)
L': (4-2, -2+4) = (2, 2)
To translate the triangle 4 units up, add 4 to the y-coordinate of each vertex:
J': (-4, 1+4) = (-4, 5)
K': (-1, 3+4) = (-1, 7)
L': (2, 2+4) = (2, 6)
Therefore, the coordinates of the vertices of the translated triangle △J'K'L' are J'(-4, 5), K'(-1, 7), and L'(2, 6).
To translate the triangle 2 units left and 4 units up, we need to subtract 2 from the x-coordinates of each vertex and add 4 to the y-coordinates of each vertex.
The coordinates of J' will be:
x-coordinate: -2 - 2 = -4
y-coordinate: -3 + 4 = 1
So, J' is (-4, 1)
The coordinates of K' will be:
x-coordinate: 1 - 2 = -1
y-coordinate: -1 + 4 = 3
So, K' is (-1, 3)
The coordinates of L' will be:
x-coordinate: 4 - 2 = 2
y-coordinate: -2 + 4 = 2
So, L' is (2, 2)
Therefore, the coordinates of the vertices of the translated triangle △J'K'L' are J'(-4, 1), K'(-1, 3), and L'(2, 2).
To translate a shape on a coordinate plane, we need to apply the same translation to each vertex of the shape.
Given that the triangle is translated 2 units left and 4 units up, we can determine the coordinates of the translated vertices as follows:
For vertex J:
- Original x-coordinate: -2
- Translation: 2 units left
- New x-coordinate: -2 - 2 = -4
- Original y-coordinate: -3
- Translation: 4 units up
- New y-coordinate: -3 + 4 = 1
Therefore, the coordinates of vertex J' are (-4, 1).
For vertex K:
- Original x-coordinate: 1
- Translation: 2 units left
- New x-coordinate: 1 - 2 = -1
- Original y-coordinate: -1
- Translation: 4 units up
- New y-coordinate: -1 + 4 = 3
Therefore, the coordinates of vertex K' are (-1, 3).
For vertex L:
- Original x-coordinate: 4
- Translation: 2 units left
- New x-coordinate: 4 - 2 = 2
- Original y-coordinate: -2
- Translation: 4 units up
- New y-coordinate: -2 + 4 = 2
Therefore, the coordinates of vertex L' are (2, 2).
Hence, the coordinates of the vertices of the translated triangle △J'K'L' are J'(-4, 1), K'(-1, 3), and L'(2, 2).