Question

a vertical translation up 4 units translates point $j(3, - 5)$ to point $j$. what are the coordinates of $j$?
$j(-1, - 5)$
$j(7, - 5)$
$j(3, - 9)$
$j(3, - 1)$

Explanation:

Step1: Recall translation rule for vertical shift

In a vertical translation, the x - coordinate remains the same and the y - coordinate changes. The rule for a vertical translation up by \(k\) units for a point \((x,y)\) is \((x,y + k)\).

Step2: Identify the values of \(x\), \(y\) and \(k\)

Given point \(J(3,- 5)\), so \(x = 3\), \(y=-5\) and \(k = 4\) (since it is a translation up 4 units).

Step3: Calculate the new y - coordinate

The new y - coordinate is \(y'=y + k=-5 + 4=-1\), and the x - coordinate remains \(x'=x = 3\). So the coordinates of \(J'\) are \((3,-1)\).

Answer:

J'(3, -1)