Question

1. triangle abc is defined by the coordinates ( a(5,1) ), ( b(3,-1) ), and ( c(2,4) ).

a. draw triangle r in the coordinate plane on the right.

b. triangle abc is translated 2 units left and then reflected over the ( y )-axis to create triangle ( abc ). draw triangle ( abc ) in the same coordinate plane and label it.

Explanation:

Step1: Plot the original triangle

To draw triangle \(ABC\) with \(A(5,1)\), \(B(3, - 1)\), and \(C(2,4)\) on the coordinate plane:

• For point \(A\), move 5 units to the right along the \(x\) - axis and 1 unit up along the \(y\) - axis.
• For point \(B\), move 3 units to the right along the \(x\) - axis and 1 unit down along the \(y\) - axis.
• For point \(C\), move 2 units to the right along the \(x\) - axis and 4 units up along the \(y\) - axis. Then connect the three points.

Step2: Translate the triangle

The rule for a translation of 2 units left is \((x,y)\to(x - 2,y)\).

• For \(A(5,1)\): \(A'(5-2,1)=(3,1)\)
• For \(B(3,-1)\): \(B'(3 - 2,-1)=(1,-1)\)
• For \(C(2,4)\): \(C'(2-2,4)=(0,4)\)

Step3: Reflect the translated triangle

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

• For \(A'(3,1)\): \(A''(-3,1)\)
• For \(B'(1,-1)\): \(B''(-1,-1)\)
• For \(C'(0,4)\): \(C''(0,4)\) (since \(x = 0\), \( - x=0\))

Then plot the points \(A''(-3,1)\), \(B''(-1,-1)\), \(C''(0,4)\) and connect them to get triangle \(A'B'C'\)

Answer:

For part (a), plot \(A(5,1)\), \(B(3,-1)\), \(C(2,4)\) and connect them. For part (b), plot \(A''(-3,1)\), \(B''(-1,-1)\), \(C''(0,4)\) and connect them.