Question

independent practice:
part a: describe the transformation that maps \\( \triangle j k l \\) to \\( \triangle p q r \\).
part b: algebraically represent the transformation needed to map \\( \triangle j k l \\) to \\( \triangle p q r \\).

Explanation:

Part A:

Step1: Analyze the transformation type

By observing the positions of the triangles \(\triangle JKL\) and \(\triangle PQR\) on the coordinate - plane, we can see that it is a translation. Translation is a transformation that moves every point of a figure or space by the same distance in a given direction.

Part B:

Step1: Find the vertical translation

Let's assume a general point \((x,y)\) in \(\triangle JKL\). If we compare the \(y\) - coordinates of corresponding points (for example, assume a point \(A(x_1,y_1)\) in \(\triangle JKL\) and its corresponding point \(A'(x_1,y_2)\) in \(\triangle PQR\)). Counting the number of units between the two triangles vertically. We find that the vertical shift is \(k\) units up. If we assume a point \(J\) (lower - left point of \(\triangle JKL\)) and \(P\) (lower - left point of \(\triangle PQR\)), by counting the units on the \(y\) - axis, we can see that the vertical translation is \(6\) units up.
The algebraic representation of a vertical translation of \(k\) units up for a point \((x,y)\) is \((x,y)\to(x,y + 6)\)

Answer:

• Part A: The transformation is a translation.
• Part B: The algebraic representation is \((x,y)\to(x,y + 6)\)