LEAP 2025 Geometry Additional & Supporting Content. Practice it free.

Corresponding angles are congruent: $3x+16=2x+34$, so $x=18$. Each angle measures $3(18)+16=70°$.

A translation is a rigid transformation that moves every point of a figure the exact same distance in the same direction. Since all points in the image remain equidistant from the points in the preimage, the figure remains congruent. In this example, a point is never kept in the same place.

The center is $(9, 2)$ and the radius is $8\textsf{.}$ A point on the circle must satisfy $2 - 8 \le b \le 2 + 8\textsf{,}$ so $-6 \le b \le 10\textsf{.}$ The value $4$ is in this interval.

$y$-coordinate $= \dfrac{10 + 2}{2} = \dfrac{12}{2} = 6$.

Parallel lines have the same slope, so $m = \dfrac{2}{3}$. Substitute $(-3, 4)$ into $y = \dfrac{2}{3}x + b$: $4 = \dfrac{2}{3}(-3) + b = -2 + b$, so $b = 6$. The equation is $y = \dfrac{2}{3}x + 6\textsf{.}$

Parallel lines have the same slope. In $y = -x + 11$, the slope is $-1$, so the slope of line $b$ is also $-1\textsf{.}$

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 9 \times 5 = 45$.

The radius is $6$ inches. $V = \pi r^{2} h = \pi (6)^{2}(20) = 720\pi$ cubic inches.