Question

the vertices of △abc are a(1, 2), b(5, 1), c(5, 4). translate △abc using the given vector. graph △abc and its image 1) x, y)->(x - 5, y) 2) x, y)->(x - 2, y - 3)

Explanation:

Step1: Translate point A for first vector

For point A(1, 2) and the vector (x, y)→(x - 5, y), substitute x = 1 and y = 2. We get A'(1 - 5, 2)=A'(-4, 2).

Step2: Translate point B for first vector

For point B(5, 1) and the vector (x, y)→(x - 5, y), substitute x = 5 and y = 1. We get B'(5 - 5, 1)=B'(0, 1).

Step3: Translate point C for first vector

For point C(5, 4) and the vector (x, y)→(x - 5, y), substitute x = 5 and y = 4. We get C'(5 - 5, 4)=C'(0, 4).

Step4: Translate point A for second vector

For point A(1, 2) and the vector (x, y)→(x - 2, y - 3), substitute x = 1 and y = 2. We get A''(1 - 2, 2 - 3)=A''(-1, -1).

Step5: Translate point B for second vector

For point B(5, 1) and the vector (x, y)→(x - 2, y - 3), substitute x = 5 and y = 1. We get B''(5 - 2, 1 - 3)=B''(3, -2).

Step6: Translate point C for second vector

For point C(5, 4) and the vector (x, y)→(x - 2, y - 3), substitute x = 5 and y = 4. We get C''(5 - 2, 4 - 3)=C''(3, 1).

To graph, plot the original points A(1, 2), B(5, 1), C(5, 4) and their translated points A', B', C' for the first vector and A'', B'', C'' for the second vector on the given coordinate - planes.

Answer:

For the vector (x, y)→(x - 5, y): A'(-4, 2), B'(0, 1), C'(0, 4).
For the vector (x, y)→(x - 2, y - 3): A''(-1, -1), B''(3, -2), C''(3, 1).