Question

1. practice triangle 1 has the following vertices. a (3,-1) b (1,-4) c (6,-5) a. on the grid provided, sketch triangle 1. b. translate triangle 1. translate it 7 units up and 8 units to the left. sketch the new image, label the image as triangle 2, and label each vertex. c. write the coordinates of the translated triangle. d. write a general rule that will transform any point on triangle 1 to a point on triangle 2.

Explanation:

Step1: Sketch triangle 1

Locate points A(3, - 1), B(1, - 4), C(6, - 5) on the grid and connect them to form triangle 1.

Step2: Apply translation rule for each vertex

The translation rule for moving 7 units up and 8 units to the left is \((x,y)\to(x - 8,y + 7)\).
For point A(3,-1): \(x=3,y = - 1\), new \(x=3-8=-5\), new \(y=-1 + 7=6\), new point A'(-5,6).
For point B(1,-4): \(x = 1,y=-4\), new \(x=1-8=-7\), new \(y=-4 + 7=3\), new point B'(-7,3).
For point C(6,-5): \(x = 6,y=-5\), new \(x=6-8=-2\), new \(y=-5 + 7=2\), new point C'(-2,2).

Step3: Sketch triangle 2

Locate points A'(-5,6), B'(-7,3), C'(-2,2) on the grid and connect them to form triangle 2.

Step4: Write general rule

The general rule for the translation is \((x,y)\to(x - 8,y + 7)\)

Answer:

a. Sketch triangle 1 by plotting A(3, - 1), B(1, - 4), C(6, - 5) and connecting them.
b. Sketch triangle 2 by plotting A'(-5,6), B'(-7,3), C'(-2,2) and connecting them.
c. Coordinates of translated triangle: A'(-5,6), B'(-7,3), C'(-2,2)
d. General rule: \((x,y)\to(x - 8,y + 7)\)