Question

find the distance between each pair of points. round to the nearest hundredth.

1. (6, - 2) and (4, - 1)
2. (-4, 5) and (4, 0)

given the graph below, find gh.
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find the mid - point between each pair of points.

1. (-1, -5) and (-5, 9)
2. (7, -2) and (-4, 2)

1. if m is the midpoint of $overline{xy}$, find the coordinates of x if m(-3, -1) and y(-8, 6).

1. if r is the midpoint of $overline{qs}$, $qr = 8x - 51$ and $rs = 3x - 6$, find qs.

Explanation:

12.

Step1: Recall distance - formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let \((x_1,y_1)=(6, - 2)\) and \((x_2,y_2)=(4,-1)\).
\[d=\sqrt{(4 - 6)^2+(-1+2)^2}\]

Step2: Simplify the expression

First, calculate \((4 - 6)^2=(-2)^2 = 4\) and \((-1 + 2)^2=1^2 = 1\). Then \(d=\sqrt{4 + 1}=\sqrt{5}\approx2.24\)

Step1: Apply distance - formula

Let \((x_1,y_1)=(-4,5)\) and \((x_2,y_2)=(4,0)\). Using \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), we have \(d=\sqrt{(4 + 4)^2+(0 - 5)^2}\)

Step2: Simplify the expression

\((4 + 4)^2=8^2 = 64\) and \((0 - 5)^2=(-5)^2 = 25\). Then \(d=\sqrt{64+25}=\sqrt{89}\approx9.43\)

Step1: Identify coordinates

Assume \(G(x_1,y_1)\) and \(H(x_2,y_2)\) from the graph. Let \(G(-3,-2)\) and \(H(0,3)\)

Step2: Use distance - formula

\(d=\sqrt{(0 + 3)^2+(3 + 2)^2}=\sqrt{3^2+5^2}=\sqrt{9 + 25}=\sqrt{34}\approx5.83\)

Answer:

\(2.24\)

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