Math / Geometry

QuestionIn the coordinate plane, the point $A(-2,2)$ is translated to the point $A^{\prime}(0,3)$ . Under the same translation, the points $B(1,5)$ and $C(-5,0)$ are translated to $B^{\prime}$ and $C^{\prime}$ , respectively. What are the coordinates of $B^{\prime}$ and $C^{\prime}$ ? B. (1) c.(1)

Studdy Solution

STEP 1

1. The translation is consistent for all points in the plane.
2. The translation vector can be determined from the movement of point $A$ to $A'$ .

STEP 2

1. Determine the translation vector.
2. Apply the translation vector to point $B$ .
3. Apply the translation vector to point $C$ .

STEP 3

Determine the translation vector by comparing the coordinates of $A$ and $A'$ :
The point $A(-2, 2)$ is translated to $A'(0, 3)$ .
Translation vector $\vec{v} = (0 - (-2), 3 - 2) = (2, 1)$ .

STEP 4

Apply the translation vector $\vec{v} = (2, 1)$ to point $B(1, 5)$ :
$B' = (1 + 2, 5 + 1) = (3, 6)$

STEP 5

Apply the translation vector $\vec{v} = (2, 1)$ to point $C(-5, 0)$ :
$C' = (-5 + 2, 0 + 1) = (-3, 1)$
The coordinates of $B'$ are $\boxed{(3, 6)}$ and the coordinates of $C'$ are $\boxed{(-3, 1)}$ .

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