NJSLA Geometry Expressing Geometric Properties with Equations Practice

Expressing Geometric Properties with Equations skills

G.GPE.A.1 Derive the equation of a line

G.GPE.B.4-7 Coordinate proofs, slope criteria, partitions, and area/perimeter

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playmedium

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

The diameter length is $\sqrt{(6 - 0)^2 + (8 - 0)^2} = \sqrt{36 + 64} = \sqrt{100} = 10\textsf{.}$ The radius is half the diameter, so $r = \dfrac{10}{2} = 5\textsf{.}$

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

The graph of the equation $(x - 9)^2 + (y - 2)^2 = 64$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $b\textsf{?}$

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.

Practice playeasy

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

The right side is $r^{2} = 16\textsf{,}$ so the radius measures $4$ units.

Practice playeasy

Find the midpoint of $(4, 6)$ and $(10, 2)$ . What is the $x$ -coordinate?

$x$ -coordinate $= \dfrac{4 + 10}{2} = \dfrac{14}{2} = 7$ .

Practice playmedium

The equation of a line is $y = \dfrac{2}{3}x + 5$ . Which equation represents the line that is parallel to this line and passes through the point $(-3, 4)$ ?

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 $y = \dfrac{2}{3}x + 6\textsf{.}$

Practice playeasy

Line $a$ is defined by $y = -x + 11$ . Line $b$ is parallel to line $a$ in the coordinate plane. What is the slope of line $b$ ?

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

Practice playmedium

A circle in the coordinate plane has a diameter with endpoints $(1, -3)$ and $(13, 13)\textsf{.}$ What is the radius of the circle?

The diameter length is $\sqrt{(13 - 1)^2 + (13 - (-3))^2} = \sqrt{12^2 + 16^2} = \sqrt{144 + 256} = \sqrt{400} = 20\textsf{.}$ The radius is half the diameter, so $r = \dfrac{20}{2} = 10\textsf{.}$