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

Explanation:

Step1: Translate left

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

Step2: Translate right

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

Step3: Translate up

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

Step4: Translate down

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

Answer:

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