Question

What are the coordinates of $\Delta ABC$ after undergoing the following transformations?



$1$. Translation of two units toward the right and then two units upward
$2$. Rotation of $90°$ counterclockwise about the origin
(Hint: All transformations happen from the point of origin.)

• A. $A^{\prime \prime }(4,-12),B^{\prime \prime }(6,-6),C^{\prime \prime }(6,-12)$
• B. $A^{\prime \prime }(12,-4),B^{\prime \prime }(6,-6),C^{\prime \prime }(12,-6)$
• C. $A^{\prime \prime }(-4,12),B^{\prime \prime }(-6,6),C^{\prime \prime }(-6,12)$
• D. $A^{\prime \prime }(-12,4),B^{\prime \prime }(-6,6),C^{\prime \prime }(-12,6)$

Answer 1

The correct option is C $A^{\prime \prime }(-4,12),B^{\prime \prime }(-6,6),C^{\prime \prime }(-6,12)$

The coordinates of $\Delta ABC$ are: $A(10,2),B(4,4),C(10,4)$

$1$. Translation of two units toward the right and then two units upward:
$A(10,2)\to$ A'(10+2, 2+2) $\to A^{\prime }(12,4)$
$B(4,4)\to$ B'(4+2, 4+2) $\to B^{\prime }(6,6)$
$C(10,4)\to$ C'(10+2, 4+2) $\to C^{\prime }(12,6)$


$2$. Rotation of $90°$ counterclockwise about the origin:
$A^{\prime }(12,4)$ $\to$ counterclockwise $\to A^{\prime \prime }(-4,12)$
$B^{\prime }(6,6)$ $\to$ counterclockwise $\to B^{\prime \prime }(-6,6)$
$C^{\prime }(12,6)$ $\to$ counterclockwise $\to C^{\prime \prime }(-6,12)$