Question

Determine the final quadrant of a point $(9,-3)$ after it is dilated by a scale factor of $-\frac{1}{3}$.

• A. Quadrant I
• B. Quadrant III
• C. Quadrant IV
• D. Quadrant II

Answer 1

The correct option is D Quadrant II

In dilation, coordinates of a point is multiplied by the scale factor.

Coordinate of the given point is $(9,-3)$.
Scale factor = $-\frac{1}{3}$

Final $x$-coordinate
= $9\times (-\frac{1}{3})=-3$

Final $y$-coordinate
= $(-3)\times (-\frac{1}{3})=1$

$\therefore$ The final coordinate = $(-3,1)$

$(-3,1)$ lies in quadrant II.

Hence, after dilation, the point will lie in quadrant II.