Question

question 1 (essay worth 10 points) (ma 912 gr 2.2 ma 912 gr 2.5 hc) triangle abc has vertices a(-3, 1), b(-3, 4), and c(-7, 1). 1 part a: if △abc is translated according to the rule (x, y)→(x - 4, y + 3) to form △abc, how is the translation described with words? (3 points) 2 part b: where are the vertices of △abc located? show your work or explain your steps (4 points) 3 part c: triangle abc is rotated 90° clockwise about the origin to form △abc. is △abc congruent to △abc? give details to support your answer. (3 points)

Explanation:

Part A:

In a coordinate translation rule \((x,y)\to(x - a,y + b)\), \(a\) represents horizontal movement (\(a>0\) is left, \(a < 0\) is right) and \(b\) represents vertical movement (\(b>0\) is up, \(b < 0\) is down). Here \(a = 4\) and \(b=3\).

A translation and a rotation are rigid transformations. Rigid transformations preserve side - lengths and angle - measures.

Answer:

The translation is \(4\) units to the left and \(3\) units up.

Part B:

Step1: Translate vertex \(A(-3,1)\)

For \(x\) - coordinate: \(x=-3-4=-7\), for \(y\) - coordinate: \(y = 1+3=4\). So \(A'(-7,4)\)

Step2: Translate vertex \(B(-3,4)\)

For \(x\) - coordinate: \(x=-3 - 4=-7\), for \(y\) - coordinate: \(y=4 + 3=7\). So \(B'(-7,7)\)

Step3: Translate vertex \(C(-7,1)\)

For \(x\) - coordinate: \(x=-7-4=-11\), for \(y\) - coordinate: \(y=1 + 3=4\). So \(C'(-11,4)\)