Question

directions: calculate the distance between each set of points below. round all answers to the nearest hundredth when necessary. 3) (-9, 4) and (-5, 2) 4) (-11, 7) and (-8, 6) 5) (-1, -2) and (-10, 12) 6) 7)

Explanation:

1. Recall the distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\):

• The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

1. For the points \((-9,4)\) and \((-5,2)\):

• Let \((x_1,y_1)=(-9,4)\) and \((x_2,y_2)=(-5,2)\).
• First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
• \(x_2 - x_1=-5-(-9)=-5 + 9 = 4\).
• \(y_2 - y_1=2 - 4=-2\).
• Then, use the distance formula:
• \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{4^2+(-2)^2}=\sqrt{16 + 4}=\sqrt{20}\approx4.47\).

1. For the points \((-11,7)\) and \((-8,6)\):

• Let \((x_1,y_1)=(-11,7)\) and \((x_2,y_2)=(-8,6)\).
• Calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
• \(x_2 - x_1=-8-(-11)=-8 + 11 = 3\).
• \(y_2 - y_1=6 - 7=-1\).
• Use the distance formula:
• \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{3^2+(-1)^2}=\sqrt{9 + 1}=\sqrt{10}\approx3.16\).

1. For the points \((-1,-2)\) and \((-10,12)\):

• Let \((x_1,y_1)=(-1,-2)\) and \((x_2,y_2)=(-10,12)\).
• Calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
• \(x_2 - x_1=-10-(-1)=-10 + 1=-9\).
• \(y_2 - y_1=12-(-2)=12 + 2 = 14\).
• Use the distance formula:
• \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(-9)^2+14^2}=\sqrt{81+196}=\sqrt{277}\approx16.64\).

Answer:

• The distance between \((-9,4)\) and \((-5,2)\) is approximately \(4.47\).
• The distance between \((-11,7)\) and \((-8,6)\) is approximately \(3.16\).
• The distance between \((-1,-2)\) and \((-10,12)\) is approximately \(16.64\).