Question

drag each set of coordinates to the correct location on the table. calculate the distance between the pairs of coordinates, and classify them according to the distance between them. (3, 4) and (2, 1) (3, 7) and (5, 2) (5, -2) and (3, 3) (-2, 3) and (1, 2) (-4, -2) and (-3, 1) (4, -1) and (-1, 1)

Explanation:

1. First, use the distance - formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\):

• For the points \((x_1,y_1)=(3,4)\) and \((x_2,y_2)=(2,1)\):
• \(d=\sqrt{(2 - 3)^2+(1 - 4)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}\).
• For the points \((x_1,y_1)=(3,7)\) and \((x_2,y_2)=(5,2)\):
• \(d=\sqrt{(5 - 3)^2+(2 - 7)^2}=\sqrt{2^2+(-5)^2}=\sqrt{4 + 25}=\sqrt{29}\).
• For the points \((x_1,y_1)=(5,-2)\) and \((x_2,y_2)=(3,3)\):
• \(d=\sqrt{(3 - 5)^2+(3+2)^2}=\sqrt{(-2)^2+5^2}=\sqrt{4 + 25}=\sqrt{29}\).
• For the points \((x_1,y_1)=(-2,3)\) and \((x_2,y_2)=(1,2)\):
• \(d=\sqrt{(1 + 2)^2+(2 - 3)^2}=\sqrt{3^2+(-1)^2}=\sqrt{9 + 1}=\sqrt{10}\).
• For the points \((x_1,y_1)=(-4,-2)\) and \((x_2,y_2)=(-3,1)\):
• \(d=\sqrt{(-3 + 4)^2+(1 + 2)^2}=\sqrt{1^2+3^2}=\sqrt{1 + 9}=\sqrt{10}\).
• For the points \((x_1,y_1)=(4,-1)\) and \((x_2,y_2)=(-1,1)\):
• \(d=\sqrt{(-1 - 4)^2+(1 + 1)^2}=\sqrt{(-5)^2+2^2}=\sqrt{25 + 4}=\sqrt{29}\).

1. Then, classify the pairs:

• \(\sqrt{10}\) units: \((3,4)\) and \((2,1)\), \((-2,3)\) and \((1,2)\), \((-4,-2)\) and \((-3,1)\).
• \(\sqrt{29}\) units: \((3,7)\) and \((5,2)\), \((5,-2)\) and \((3,3)\), \((4,-1)\) and \((-1,1)\).

Answer:

\(\sqrt{10}\) units: \((3,4)\) and \((2,1)\), \((-2,3)\) and \((1,2)\), \((-4,-2)\) and \((-3,1)\)
\(\sqrt{29}\) units: \((3,7)\) and \((5,2)\), \((5,-2)\) and \((3,3)\), \((4,-1)\) and \((-1,1)\)