Question

1. fernanda wants to draw line segments to connect the points to form a shape. what would be the most appropriate tool for her to use? 17. what is the name of the shape fernanda forms by connecting the points? be as specific as possible.

Explanation:

Step1: Determine the tool for connecting points

To connect points \(D(1,1)\), \(E(4,1)\), \(F(3,3)\), \(G(2,3)\) on a coordinate - grid, the most appropriate tool is a ruler. A ruler is used to draw straight - line segments between points.

Step2: Identify the shape

• Calculate the lengths of the sides:
• The length of \(DE\): Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(D(1,1)\) and \(E(4,1)\), \(d_{DE}=\sqrt{(4 - 1)^2+(1 - 1)^2}=\sqrt{9+0}=3\)
• The length of \(EF\): For \(E(4,1)\) and \(F(3,3)\), \(d_{EF}=\sqrt{(3 - 4)^2+(3 - 1)^2}=\sqrt{1 + 4}=\sqrt{5}\)
• The length of \(FG\): For \(F(3,3)\) and \(G(2,3)\), \(d_{FG}=\sqrt{(2 - 3)^2+(3 - 3)^2}=\sqrt{1+0}=1\)
• The length of \(GD\): For \(G(2,3)\) and \(D(1,1)\), \(d_{GD}=\sqrt{(1 - 2)^2+(1 - 3)^2}=\sqrt{1+4}=\sqrt{5}\)
• The slope of \(DE\): \(m_{DE}=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1 - 1}{4 - 1}=0\) (horizontal line)
• The slope of \(FG\): \(m_{FG}=\frac{3 - 3}{2 - 3}=0\) (horizontal line)
• The slope of \(EF\): \(m_{EF}=\frac{3 - 1}{3 - 4}=- 2\)
• The slope of \(GD\): \(m_{GD}=\frac{1 - 3}{1 - 2}=2\)
• Since \(DE\parallel FG\) and \(EF = GD\), the shape is a parallelogram

Answer:

1. Ruler
2. Parallelogram