Question

the coordinates of midpoint m and endpoint c of a segment are m(25.4, 60.1) and c(18.3, 72.5). find the coordinates of the other endpoint.

(11.2, 84.9)
(21.85, 66.3)
(32.5, 47.7)
(37.8, 53)

Explanation:

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<reasoning>

Set up midpoint equations for the unknown endpoint \(D(x, y)\)

\[

$$\begin{aligned} M(x_m, y_m) &= (25.4, 60.1) \\ C(x_c, y_c) &= (18.3, 72.5) \\ \frac{x + 18.3}{2} &= 25.4 \\ \frac{y + 72.5}{2} &= 60.1 \end{aligned}$$

\]

Solve for the x-coordinate

\[

$$\begin{aligned} x + 18.3 &= 50.8 \\ x &= 50.8 - 18.3 \\ x &= 32.5 \end{aligned}$$

\]

Solve for the y-coordinate

\[

$$\begin{aligned} y + 72.5 &= 120.2 \\ y &= 120.2 - 72.5 \\ y &= 47.7 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \((11.2, 84.9)\)</mcq-option>
<mcq-option>(B) \((21.85, 66.3)\)</mcq-option>
<mcq-correct>(C) \((32.5, 47.7)\)</mcq-correct>
<mcq-option>(D) \((37.8, 53)\)</mcq-option>
</answer>

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Answer:

<pre_analysis>
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</pre_analysis>

<reasoning>

Set up midpoint equations for the unknown endpoint \(D(x, y)\)

\[

$$\begin{aligned} M(x_m, y_m) &= (25.4, 60.1) \\ C(x_c, y_c) &= (18.3, 72.5) \\ \frac{x + 18.3}{2} &= 25.4 \\ \frac{y + 72.5}{2} &= 60.1 \end{aligned}$$

\]

Solve for the x-coordinate

\[

$$\begin{aligned} x + 18.3 &= 50.8 \\ x &= 50.8 - 18.3 \\ x &= 32.5 \end{aligned}$$

\]

Solve for the y-coordinate

\[

$$\begin{aligned} y + 72.5 &= 120.2 \\ y &= 120.2 - 72.5 \\ y &= 47.7 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \((11.2, 84.9)\)</mcq-option>
<mcq-option>(B) \((21.85, 66.3)\)</mcq-option>
<mcq-correct>(C) \((32.5, 47.7)\)</mcq-correct>
<mcq-option>(D) \((37.8, 53)\)</mcq-option>
</answer>

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]
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