Question

1. let p be a point with coordinates (a,b), and assume that c and d are positive numbers. (a) translate the point p by c units in the x - direction to obtain a point q, then translate q by d units in the y - direction to obtain the point r. what are the coordinates of the point r?

Explanation:

Step1: Translate point P in x - direction

When we translate a point $(x,y)$ by $c$ units in the $x$-direction, the new $x$-coordinate is $x + c$ and the $y$-coordinate remains the same. Given point $P(a,b)$, after translating it by $c$ units in the $x$-direction, the coordinates of point $Q$ are $(a + c,b)$.

Step2: Translate point Q in y - direction

When we translate a point $(x,y)$ by $d$ units in the $y$-direction, the $x$-coordinate remains the same and the new $y$-coordinate is $y + d$. Since point $Q$ has coordinates $(a + c,b)$, after translating it by $d$ units in the $y$-direction, the coordinates of point $R$ are $(a + c,b + d)$.

Answer:

$(a + c,b + d)$