Translation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

medium

Triangle with vertices

A(1,2)

B(4,2)

C(3,5)

is translated by

\langle -3, 4 \rangle

. Find the new vertices.

1
Apply the translation vector $\langle -3, 4 \rangle$ to each vertex by adding $-3$ to the $x$ -coordinate and $4$ to the $y$ -coordinate.
2
$A' = (1 + (-3),\; 2 + 4) = (-2, 6)$ . $B' = (4 + (-3),\; 2 + 4) = (1, 6)$ . $C' = (3 + (-3),\; 5 + 4) = (0, 9)$ .
3
Verify: the side lengths are preserved. $AB = 3$ , $A'B' = |1 - (-2)| = 3$ \checkmark. The triangle shifted 3 units left and 4 units up.

Answer

A'(-2, 6),\; B'(1, 6),\; C'(0, 9)

A translation moves every point by the same vector. Add the horizontal component to each

x

-coordinate and the vertical component to each

y

-coordinate. The shape, size, and orientation of the figure remain unchanged.

About Translation

A rigid transformation that slides every point of a figure the same distance in the same direction.

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