Sovi AI

Aufgabe

Lösungsschritte

1. Understand the question

   $\\overline{pq}$ is reflected across the line $x=-3$. the coordinates of the endpoints of the image of $\\overline{pq}$ are $p(5, 2)$ and $q(2, 4)$. what are the coordinates of $q$?
   a $(1,4)$
   b $(-3,4)$
   c $(5,4)$
   d $(-8,4)$

2. Explanation

   Step1: Recall reflection rule for $x=k$

   For a point $(x,y)$ reflected over $x=k$, the pre-image $x$-coordinate satisfies $k = \frac{x + x'}{2}$, where $x'$ is the image $x$-coordinate. The $y$-coordinate stays the same.

   Step2: Identify known values for $Q'$

   We have $k=-3$, $x'=2$, $y'=4$.

   Step3: Solve for pre-image $x$-coordinate

   Rearrange the formula: $x = 2k - x'$
   Substitute values: $x = 2(-3) - 2 = -6 - 2 = -8$

   Step4: Determine $y$-coordinate of $Q$

   Since reflection over vertical line preserves $y$-coordinate, $y = y' = 4$.

3. Final answer

   D. $(-8, 4)$

Antwort

Question Analysis

OCR Text

$\\overline{pq}$ is reflected across the line $x=-3$. the coordinates of the endpoints of the image of $\\overline{pq}$ are $p(5, 2)$ and $q(2, 4)$. what are the coordinates of $q$?
a $(1,4)$
b $(-3,4)$
c $(5,4)$
d $(-8,4)$

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