Question

translate \\( \triangle r s t \\) 5 units to the left to form \\( \triangle r ^ { prime } s ^ { prime } t ^ { prime } \\).
where will the image of \\( \triangle r s t \\) be located?
quadrant i
quadrant ii
quadrant iii
quadrant iv

Explanation:

Step1: Recall the rule for horizontal translation

When a point \((x,y)\) is translated \(a\) units to the left, the new coordinates are \((x - a,y)\). Here \(a = 5\).

Step2: Analyze the original quadrant

The original \(\triangle RST\) is in Quadrant I (where \(x>0,y>0\)). After translation \(5\) units to the left, the \(x -\)coordinates of all points of \(\triangle RST\) will decrease by \(5\). Let's assume a general point \((x,y)\) in \(\triangle RST\) with \(x>0\). After translation, the new \(x-\)coordinate is \(x - 5\). For some points, if \(x-5<0\) and \(y>0\), the points will move to Quadrant II.

Answer:

Quadrant II