Question

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

Explanation:

Step1: Translate left

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

Step2: Translate right

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

Step3: Translate up

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

Step4: Translate down

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

Answer:

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