Question

b(1, -7), c(-3, -8)
f(3, 2), g(2, -1)
j(-5, 4), k(-7, 1)
follow the directions below.
(a) find the length of each segment.
give an exact answer (not a decimal approximation).
bc =
fg =
jk =
(b) check all statements that are true below.
□ \overline{bc} \cong \overline{fg}
□ \overline{bc} \cong \overline{jk}
□ \overline{fg} \cong \overline{jk}
□ none of these are true

Explanation:

Step1: Use the distance formula

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

Step2: Calculate \(BC\)

For \(B(1,-7)\) and \(C(-3,-8)\), \(x_1 = 1,y_1=-7,x_2=-3,y_2 = -8\)

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Step3: Calculate \(FG\)

For \(F(3,2)\) and \(G(2,-1)\), \(x_1 = 3,y_1=2,x_2=2,y_2=-1\)

$$
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Step4: Calculate \(JK\)

For \(J(-5,4)\) and \(K(-7,1)\), \(x_1=-5,y_1 = 4,x_2=-7,y_2=1\)

$$
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Step5: Check congruence

Segments are congruent if they have the same length. Since \(\sqrt{17}
eq\sqrt{10}
eq\sqrt{13}\)

Answer:

(a) \(BC=\sqrt{17}\), \(FG=\sqrt{10}\), \(JK=\sqrt{13}\)
(b) None of these are true