Question

translate this triangle $(x,y)\to(x + 5,y + 10)$

pre-image
coordinatesnew xnew y
$(-2,-2)$
$(2,1)$
$(1,-5)$

Explanation:

Step1: Calculate new \(x\) - coordinate for \((-2,-2)\)

For the \(x\) - coordinate, use the rule \(x\to x + 5\). Substitute \(x=-2\) into \(x + 5\), so \(-2+5 = 3\).

Step2: Calculate new \(y\) - coordinate for \((-2,-2)\)

For the \(y\) - coordinate, use the rule \(y\to y + 10\). Substitute \(y = - 2\) into \(y + 10\), so \(-2+10=8\).

Step3: Calculate new \(x\) - coordinate for \((2,1)\)

Substitute \(x = 2\) into \(x + 5\), so \(2+5=7\).

Step4: Calculate new \(y\) - coordinate for \((2,1)\)

Substitute \(y = 1\) into \(y + 10\), so \(1 + 10=11\).

Step5: Calculate new \(x\) - coordinate for \((1,-5)\)

Substitute \(x = 1\) into \(x + 5\), so \(1+5=6\).

Step6: Calculate new \(y\) - coordinate for \((1,-5)\)

Substitute \(y=-5\) into \(y + 10\), so \(-5 + 10=5\).

Answer:

Pre - Image coordinates	New \(X\)	New \(Y\)
\((2,1)\)	\(7\)	\(11\)
\((1,-5)\)	\(6\)	\(5\)