Question

which of the following transformations represents a translation 4 units left and 7 units up?
$(x, y) \to (x - 7, y + 4)$
$(x, y) \to (x + 4, y - 7)$
$(x, y) \to (x - 4, y + 7)$
$(x, y) \to (x + 7, y - 4)$

Explanation:

Step1: Recall translation rules

In coordinate geometry, a translation of \( h \) units left/right and \( k \) units up/down is given by \((x,y)\to(x + h,y + k)\), where \( h<0 \) for left, \( h>0 \) for right, \( k>0 \) for up, \( k<0 \) for down.

Step2: Apply to 4 left, 7 up

For 4 units left, \( h=- 4\) (since left means subtract from \( x \)). For 7 units up, \( k = 7\) (since up means add to \( y \)). So the transformation is \((x,y)\to(x-4,y + 7)\).

Answer:

\((x, y) \mapsto (x - 4, y + 7)\)