$$ \overline{P Q} $$ is reflected across the line $$ x=-3 $$. The coordinates of the endpoints of the image of $$ \overline{P Q} $$ are $$ P^{\prime}(5,2) $$ and $$ Q^{\prime}(2,4) $$. What are the coordinates of $$ Q $$ ? $$ \begin{array}{l} ext { A }(1,4) \ ext { B }(-3,4) \ ext { C }(5,4) \ ext { D }(-8,4)\end{array} $$

Question

$$ \overline{P Q} $$ is reflected across the line $$ x=-3 $$. The coordinates of the endpoints of the image of $$ \overline{P Q} $$ are $$ P^{\prime}(5,2) $$ and $$ Q^{\prime}(2,4) $$. What are the coordinates of $$ Q $$ ? $$ \begin{array}{l}	ext { A }(1,4) \ 	ext { B }(-3,4) \ 	ext { C }(5,4) \ 	ext { D }(-8,4)\end{array} $$

UpStudy AI · Accepted Answer

To find the coordinates of $$ Q $$, we need to determine the reflection of $$ Q' $$ across the line $$ x = -3 $$.

**Reflection Formula:**
When reflecting a point $$(a, b)$$ across a vertical line $$ x = k $$, the reflected point $$(a', b')$$ has coordinates:
$$
a' = 2k - a \quad \text{and} \quad b' = b
$$

**Given:**
- The reflected point $$ Q' $$ has coordinates $$ (2, 4) $$.
- The line of reflection is $$ x = -3 $$.

**Applying the Formula:**
1. **Find the original $$ x $$-coordinate:**
$$
2 = 2(-3) - x \
2 = -6 - x \
x = -6 - 2 \
x = -8
$$
2. **The $$ y $$-coordinate remains the same:**
$$
y = 4
$$

**Thus, the original point $$ Q $$ is:**
$$
Q = (-8, 4)
$$

**Answer:**  
**D $$(-8, 4)$$**
The coordinates of $$ Q $$ are $$(-8, 4)$$.

is reflected across the line . The coordinates of the
endpoints of the image of are and . What
are the coordinates of ?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Geometry Questions

is reflected across the line . The coordinates of the endpoints of the image of are and . What are the coordinates of ?