Give the coordinates of $$ Q $$ under a dilation about point $$ D $$ with scale factor 4 . $$ Q(9,-3) $$ $$ D(4,-4) $$ Show your work here

Question

UpStudy AI · Accepted Answer

To find the coordinates of point $$ Q' $$ after a dilation about point $$ D $$ with a scale factor of 4, we'll follow these steps:

### Given:
- **Original Point:** $$ Q(9, -3) $$
- **Center of Dilation:** $$ D(4, -4) $$
- **Scale Factor ($$ k $$):** 4

### Dilation Formula:
When dilating a point $$ Q(x, y) $$ about a center $$ D(x_0, y_0) $$ with scale factor $$ k $$, the coordinates of the dilated point $$ Q'(x', y') $$ are given by:

$$
\begin{cases}
x' = x_0 + k \times (x - x_0) \
y' = y_0 + k \times (y - y_0)
\end{cases}
$$

### Applying the Formula:

1. **Calculate the Change in the x-coordinate:**
   $$
   x' = x_0 + k \times (x - x_0) = 4 + 4 \times (9 - 4) = 4 + 4 \times 5 = 4 + 20 = 24
   $$

2. **Calculate the Change in the y-coordinate:**
   $$
   y' = y_0 + k \times (y - y_0) = -4 + 4 \times (-3 - (-4)) = -4 + 4 \times (1) = -4 + 4 = 0
   $$

### Result:
The coordinates of the dilated point $$ Q' $$ are **$$ (24, 0) $$**.

$$
Q'(24,\ 0)
$$
The coordinates of $$ Q $$ after dilation about point $$ D $$ with a scale factor of 4 are $$ (24, 0) $$.

Give the coordinates of \( Q \) under a dilation about point \( D \) with scale factor 4 . \( Q(9,-3) \) \( D(4,-4) \) Show your work here

Solución de tutoría real

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Geometry Questions