Question

find the length of the segments below. round to the nearest tenth (1 decimal place)

Explanation:

1. For the first - segment with endpoints \((-2,-2)\) and \((1,3)\):

• Step 1: Identify the distance formula
• The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-2,y_1 = - 2,x_2 = 1,y_2=3\).
• Step 2: Calculate the differences
• First, find \(x_2 - x_1\) and \(y_2 - y_1\). \(x_2 - x_1=1-(-2)=3\) and \(y_2 - y_1=3 - (-2)=5\).
• Step 3: Square the differences and sum them
• \((x_2 - x_1)^2=3^2 = 9\) and \((y_2 - y_1)^2=5^2 = 25\). Then \((x_2 - x_1)^2+(y_2 - y_1)^2=9 + 25=34\).
• Step 4: Take the square - root and round
• \(d=\sqrt{34}\approx5.8\).

1. For the second - segment (not enough information given in the problem description about its endpoints, assume it's not relevant for now)
2. For the third - segment with endpoints \((-2,-3)\) and \((4,-4)\):

• Step 1: Identify the distance formula
• Using \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(x_1=-2,y_1=-3,x_2 = 4,y_2=-4\).
• Step 2: Calculate the differences
• \(x_2 - x_1=4-(-2)=6\) and \(y_2 - y_1=-4-(-3)=-1\).
• Step 3: Square the differences and sum them
• \((x_2 - x_1)^2=6^2 = 36\) and \((y_2 - y_1)^2=(-1)^2 = 1\). Then \((x_2 - x_1)^2+(y_2 - y_1)^2=36 + 1=37\).
• Step 4: Take the square - root and round
• \(d=\sqrt{37}\approx6.1\).

1. For the fourth - segment with endpoints \((1,3)\) and \((4,0)\):

• Step 1: Identify the distance formula
• Using \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(x_1 = 1,y_1=3,x_2 = 4,y_2=0\).
• Step 2: Calculate the differences
• \(x_2 - x_1=4 - 1=3\) and \(y_2 - y_1=0 - 3=-3\).
• Step 3: Square the differences and sum them
• \((x_2 - x_1)^2=3^2 = 9\) and \((y_2 - y_1)^2=(-3)^2 = 9\). Then \((x_2 - x_1)^2+(y_2 - y_1)^2=9+9 = 18\).
• Step 4: Take the square - root and round
• \(d=\sqrt{18}\approx4.2\).

Answer:

For the segment with endpoints \((-2,-2)\) and \((1,3)\): \(5.8\)
For the segment with endpoints \((-2,-3)\) and \((4,-4)\): \(6.1\)
For the segment with endpoints \((1,3)\) and \((4,0)\): \(4.2\)