HSG.GPE.A.1 Math Practice Questions

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(-6, -5)$ and $(-6, 9)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $x$ -coordinate, so the diameter is vertical with length $|9 - (-5)| = 14\textsf{.}$ The radius is half the diameter, so $r = \dfrac{14}{2} = 7\textsf{.}$

Practice playeasy

The equation $(x - 2)^2 + (y + 1)^2 = 16$ represents Circle A. Circle B is obtained by shifting Circle A down $3$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(2, -1)$ and radius $4$ . Shifting down $3$ moves the center to $(2, -4)$ , so Circle B is $(x - 2)^2 + (y + 4)^2 = 16$ .

Practice playeasy

A circle in the coordinate plane has equation $(x - 3)^{2} + (y + 1)^{2} = 16\textsf{.}$ What is the center of the circle?

Standard form is $(x - h)^{2} + (y - k)^{2} = r^{2}\textsf{.}$ Here $h = 3$ and $k = -1\textsf{,}$ so the center is $(3, -1)\textsf{.}$

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(2, -4)$ and $(18, -4)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $y$ -coordinate, so the diameter is horizontal with length $|18 - 2| = 16\textsf{.}$ The radius is half the diameter, so $r = \dfrac{16}{2} = 8\textsf{.}$

Practice playeasy

The equation $x^2 + (y - 6)^2 = 64$ represents Circle A. Circle B is obtained by shifting Circle A down $6$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(0, 6)$ and radius $8$ . Shifting down $6$ moves the center to the origin, so Circle B is $x^2 + y^2 = 64$ .

Practice playeasy

A circle in the coordinate plane has equation $(x + 8)^{2} + (y - 3)^{2} = 49\textsf{.}$ What is the $x$ -coordinate of the center of the circle?

$(x + 8)^{2} = (x - (-8))^{2}\textsf{,}$ so the center's $x$ -coordinate is $-8\textsf{.}$

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(8, 0)$ and $(8, 6)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $x$ -coordinate, so the diameter is vertical with length $|6 - 0| = 6\textsf{.}$ The radius is half the diameter, so $r = \dfrac{6}{2} = 3\textsf{.}$

Practice playeasy

The equation $(x - 6)^2 + y^2 = 81$ represents Circle A. Circle B is obtained by shifting Circle A left $6$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(6, 0)$ and radius $9$ . Shifting left $6$ moves the center to the origin, so Circle B is $x^2 + y^2 = 81$ .

HSG.GPE.A.1 math practice. Learn by doing.

Skills aligned to HSG.GPE.A.1

Circle diameter endpoints to radius (SAT)

Circle equation translations (ACT/SAT/PSAT 8/9/10)

Equation of a circle

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