Question

1. if a point $(x,y)$ is translated 5 units right and 4 units up, what is the new position?

$(x + 5,y + 4)$
$(x + 5,y - 4)$
$(x - 5,y + 4)$
$(x - 5,y - 4)$

Explanation:

Step1: Analyze horizontal translation

When a point is translated \(a\) units to the right, the \(x -\)coordinate of the point changes as \(x\to x + a\). Here \(a = 5\), so the \(x -\)coordinate becomes \(x+5\).

Step2: Analyze vertical translation

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

Answer:

\((x + 5,y+4)\) (the first option)