Question

match each translation of the point (1, -2) to the coordinates of its image. 3 units left, 3 units right, 3 units up, 3 units down with options (4, -2), (-2, -2), (1, 1), (1, -5)

Explanation:

Step1: Recall translation rules

For a point \((x,y)\), moving left/right changes the \(x\)-coordinate (left: \(x - a\), right: \(x + a\)), moving up/down changes the \(y\)-coordinate (up: \(y + a\), down: \(y - a\)), where \(a\) is the number of units.

Step2: Translate \((1, -2)\) 3 units left

Left: \(x = 1 - 3 = -2\), \(y\) remains \(-2\). So image is \((-2, -2)\).

Step3: Translate \((1, -2)\) 3 units right

Right: \(x = 1 + 3 = 4\), \(y\) remains \(-2\). So image is \((4, -2)\).

Step4: Translate \((1, -2)\) 3 units up

Up: \(y = -2 + 3 = 1\), \(x\) remains \(1\). So image is \((1, 1)\).

Step5: Translate \((1, -2)\) 3 units down

Down: \(y = -2 - 3 = -5\), \(x\) remains \(1\). So image is \((1, -5)\).

Answer:

• 3 units left \(

ightarrow\) \((-2, -2)\)

• 3 units right \(

ightarrow\) \((4, -2)\)

• 3 units up \(

ightarrow\) \((1, 1)\)

• 3 units down \(

ightarrow\) \((1, -5)\)