Question

1. draw the image of each figure under the given transformation. record the coordinate of the image $pqr$ on the table.

$(x,y)→(x + 1,y + 2)$
preimage
$p(-4,2)$
$q(-1,3)$
$r(-3,-3)$
image
$p$( )
$q$( )
$r$( )

Explanation:

Step1: Apply the transformation rule to \(x\)-coordinate

For a point \((x,y)\) with transformation \((x,y)\to(x + 1,y+2)\), add \(1\) to the \(x\)-coordinate of each pre - image point.

• For \(P(-4,2)\): \(x=-4\), new \(x=-4 + 1=-3\)
• For \(Q(-1,3)\): \(x=-1\), new \(x=-1 + 1=0\)
• For \(R(-3,-3)\): \(x=-3\), new \(x=-3 + 1=-2\)

Step2: Apply the transformation rule to \(y\)-coordinate

Add \(2\) to the \(y\)-coordinate of each pre - image point.

• For \(P(-4,2)\): \(y = 2\), new \(y=2+2 = 4\)
• For \(Q(-1,3)\): \(y = 3\), new \(y=3+2=5\)
• For \(R(-3,-3)\): \(y=-3\), new \(y=-3 + 2=-1\)

Answer:

\(P'(-3,4)\), \(Q'(0,5)\), \(R'(-2,-1)\)