Question

use tools use the number line to find the coordinate of the mid - point. 13. $overline{de}$ 14. $overline{bc}$ 15. $overline{bd}$ 16. $overline{ad}$

Explanation:

1. For finding the mid - point of a line segment on a number line:

• The formula for the mid - point of a line segment with endpoints \(x_1\) and \(x_2\) on a number line is \(M=\frac{x_1 + x_2}{2}\).

1. 13. For line segment \(\overline{DE}\):

• The coordinate of \(D = 8\) and the coordinate of \(E=12\).
• Step1: Identify the formula and values
• Using the mid - point formula \(M=\frac{x_1 + x_2}{2}\), where \(x_1 = 8\) and \(x_2 = 12\).
• \(M=\frac{8 + 12}{2}\).
• Step2: Calculate the sum in the numerator
• \(8+12 = 20\), so \(M=\frac{20}{2}\).
• Step3: Perform the division
• \(\frac{20}{2}=10\).

1. 14. For line segment \(\overline{BC}\):

• The coordinate of \(B=-1\) and the coordinate of \(C = 3\).
• Step1: Identify the formula and values
• Using the mid - point formula \(M=\frac{x_1 + x_2}{2}\), where \(x_1=-1\) and \(x_2 = 3\).
• \(M=\frac{-1 + 3}{2}\).
• Step2: Calculate the sum in the numerator
• \(-1+3 = 2\), so \(M=\frac{2}{2}\).
• Step3: Perform the division
• \(\frac{2}{2}=1\).

1. 15. For line segment \(\overline{BD}\):

• The coordinate of \(B=-1\) and the coordinate of \(D = 8\).
• Step1: Identify the formula and values
• Using the mid - point formula \(M=\frac{x_1 + x_2}{2}\), where \(x_1=-1\) and \(x_2 = 8\).
• \(M=\frac{-1+8}{2}\).
• Step2: Calculate the sum in the numerator
• \(-1 + 8=7\), so \(M=\frac{7}{2}=3.5\).

1. 16. For line segment \(\overline{AD}\):

• The coordinate of \(A=-4\) and the coordinate of \(D = 8\).
• Step1: Identify the formula and values
• Using the mid - point formula \(M=\frac{x_1 + x_2}{2}\), where \(x_1=-4\) and \(x_2 = 8\).
• \(M=\frac{-4 + 8}{2}\).
• Step2: Calculate the sum in the numerator
• \(-4+8 = 4\), so \(M=\frac{4}{2}\).
• Step3: Perform the division
• \(\frac{4}{2}=2\).

Answer:

1. 10
2. 1
3. 3.5
4. 2