Question

you can perform translations in the coordinate plane. translate △abc 4 units up to form △abc.
where will the image of △abc be located?
quadrant i
quadrant ii
quadrant iii
quadrant iv

Explanation:

Step1: Determine the original quadrant

Assume the original triangle \( \triangle ABC \) is in Quadrant III (since the coordinates of its vertices are negative in \(x\) and \(y\) - axis before translation).

Step2: Analyze the translation effect

A translation of \(4\) units up changes the \(y\) - coordinate of each vertex. If a point \((x,y)\) is translated \(4\) units up, its new coordinates are \((x,y + 4)\).

Step3: Determine the new quadrant

Since the \(x\) - coordinates of the vertices of \( \triangle ABC\) are negative and after adding \(4\) to the \(y\) - coordinates (translation up), the \(y\) - coordinates become non - negative. Points with \(x<0\) and \(y\geq0\) lie in Quadrant II.

Answer:

Quadrant II