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

Explanation:

Step1: Translate left

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

Step2: Translate right

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

Step3: Translate up

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

Step4: Translate down

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

Answer:

3 units left \(\to(-2,-2)\); 3 units right \(\to(4,-2)\); 3 units up \(\to(1,1)\); 3 units down \(\to(1,-5)\)