Question

△jkl congruent to △mnp; reflection in the, represented by, followed by a translation along ( ) which is represented by

Explanation:

Step1: Check Congruence

Congruent triangles have equal side lengths. By counting grid units, \(JK = NM = 2\) units, \(KL = NP = 3\) units, \(JL = MP=\sqrt{(4)^2 + (1)^2}=\sqrt{17}\) units. So \(\triangle JKL\) is congruent to \(\triangle MNP\).

Step2: Determine Reflection Axis

Reflect \(\triangle JKL\) over the \(y -\)axis. The rule for reflection over the \(y -\)axis is \((x,y)\to(-x,y)\).

Step3: Determine Translation

After reflection over the \(y -\)axis, translate the reflected triangle. The horizontal translation: from \(x=- 3\) (after reflection of \(x = 3\) for some key - points) to \(x = 1\) (for \(\triangle MNP\)) is \(x\) - direction translation. The vertical translation: no vertical change as the vertical positions (after reflection and considering base - line) for corresponding sides. The translation vector \((x,y)\to(x + 4,y)\) (since \(1-(-3)=4\) in \(x -\)direction and \(y\) - values of corresponding vertices are same).

Answer:

\(\triangle JKL\) is congruent to \(\triangle MNP\); reflection in the \(y -\)axis, represented by \((x,y)\to(-x,y)\), followed by a translation along \((x,y)\to(x + 4,y)\) ( \(x -\)direction) which is represented by the vector \(\langle4,0
angle\)