Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match each pair of points with the approximate distance between them. round your answers to the nearest tenth. 7.07 units 5.1 units 2 units 2.83 units 5.39 units 13.15 units 12.5 units (3, -1) and (5, 4) (2, 3) and (4, 5) (-5, 7) and (8, 5) (-2, 4) and (3, -1)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate distance for $(3,-1)$ and $(5,4)$

Let $(x_1,y_1)=(3,-1)$ and $(x_2,y_2)=(5,4)$. Then $d=\sqrt{(5 - 3)^2+(4+ 1)^2}=\sqrt{4 + 25}=\sqrt{29}\approx5.4$ (not an exact match in options, closest is 5.39).

Step3: Calculate distance for $(2,3)$ and $(4,5)$

Let $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(4,5)$. Then $d=\sqrt{(4 - 2)^2+(5 - 3)^2}=\sqrt{4+4}=\sqrt{8}\approx2.83$.

Step4: Calculate distance for $(-5,7)$ and $(8,5)$

Let $(x_1,y_1)=(-5,7)$ and $(x_2,y_2)=(8,5)$. Then $d=\sqrt{(8 + 5)^2+(5 - 7)^2}=\sqrt{169 + 4}=\sqrt{173}\approx13.15$.

Step5: Calculate distance for $(-2,4)$ and $(3,-1)$

Let $(x_1,y_1)=(-2,4)$ and $(x_2,y_2)=(3,-1)$. Then $d=\sqrt{(3 + 2)^2+(-1 - 4)^2}=\sqrt{25+25}=\sqrt{50}\approx7.07$.

Answer:

$(3,-1)$ and $(5,4)$ $\to$ 5.39 units
$(2,3)$ and $(4,5)$ $\to$ 2.83 units
$(-5,7)$ and $(8,5)$ $\to$ 13.15 units
$(-2,4)$ and $(3,-1)$ $\to$ 7.07 units