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
$(-2,-2)$
$(1,1)$
$(4,-2)$
$(1,-5)$

Explanation:

Step1: Horizontal translation rule

When a point \((x,y)\) is translated \(a\) units left, the new \(x\) - coordinate is \(x - a\), and \(y\) remains the same. For the point \((1,-2)\) translated \(3\) units left: \(x=1 - 3=-2\), \(y = - 2\).

Step2: Horizontal translation rule (right)

When a point \((x,y)\) is translated \(a\) units right, the new \(x\) - coordinate is \(x + a\), and \(y\) remains the same. For the point \((1,-2)\) translated \(3\) units right: \(x=1 + 3 = 4\), \(y=-2\).

Step3: Vertical translation rule (up)

When a point \((x,y)\) is translated \(a\) units up, the new \(y\) - coordinate is \(y + a\), and \(x\) remains the same. For the point \((1,-2)\) translated \(3\) units up: \(x = 1\), \(y=-2 + 3=1\).

Step4: Vertical translation rule (down)

When a point \((x,y)\) is translated \(a\) units down, the new \(y\) - coordinate is \(y - a\), and \(x\) remains the same. For the point \((1,-2)\) translated \(3\) units down: \(x = 1\), \(y=-2-3=-5\).

Answer:

• \(3\) units left: \((-2,-2)\)
• \(3\) units right: \((4,-2)\)
• \(3\) units up: \((1,1)\)
• \(3\) units down: \((1,-5)\)