Question

a triangle is drawn on the coordinate plane. it is translated 4 units right and 3 units down. which rule describes the translation?
$(x,y)\to(x + 3,y - 4)$
$(x,y)\to(x + 3,y + 4)$
$(x,y)\to(x + 4,y - 3)$
$(x,y)\to(x + 4,y + 3)$

Explanation:

Step1: Analyze horizontal translation

When a point \((x,y)\) is translated \(a\) units to the right, the \(x -\) coordinate changes as \(x\to x + a\). Here, \(a = 4\), so the \(x -\) coordinate of the point becomes \(x+4\).

Step2: Analyze vertical translation

When a point \((x,y)\) is translated \(b\) units down, the \(y -\) coordinate changes as \(y\to y - b\). Here, \(b = 3\), so the \(y -\) coordinate of the point becomes \(y - 3\).

Answer:

\((x,y)\to(x + 4,y-3)\) (the third option)