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

Explanation:

Step1: Translate 3 units left

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

Step2: Translate 3 units right

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

Step3: Translate 3 units up

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

Step4: Translate 3 units down

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

Answer:

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