Georgia Milestones Geometry Expressing Geometric Properties with Equations. Practice it free.

Students translate between algebraic and geometric representations of figures. This Geometry reporting domain maps to 8 practice skills and 8 representative questions from the playable bank.

Geometry8 mapped skills
What the test measures

Expressing Geometric Properties with Equations skills

  1. Translate between the geometric description and the equation for a conic section

  2. Use coordinates to prove simple geometric theorems algebraically

  3. Use coordinates to solve problems

Standards basis

Georgia Standards of Excellence (state-adopted content standards) — Georgia

How the Georgia Milestones reports it

Georgia Milestones is Georgia’s own statewide assessment system, aligned to Georgia’s state-adopted content standards rather than a shared national test framework. The official page says it measures knowledge and skills in the state-adopted standards for mathematics across grades 3 through high school ([Georgia Department of Education](https://gadoe.org/assessment-accountability/georgia-milestones/)).

Blueprint & weighting

Not published on the official Georgia Milestones overview page reviewed here.

Practice by skill

Topics mapped to this domain

Possible coordinates on a circle (SAT)

Grade 1010 questions

Midpoint formula

Grade 1015 questions

Parallel and perpendicular lines through a point (SAT)

Grade 910 questions

Parallel and perpendicular slopes from slope-intercept form

Grade 910 questions

Circle diameter endpoints to radius (SAT)

Grade 1010 questions

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

Grade 1010 questions

Conic sections

Grade 1120 questions

Equation of a circle

Grade 1020 questions
Try it now

8 free questions · 0/0 correct

Practice playmedium

The graph of the equation (x+8)2+(y−6)2=169(x + 8)^2 + (y - 6)^2 = 169 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for b?b\textsf{?}

The center is (−8,6)(-8, 6) and the radius is 13.13\textsf{.} A point on the circle must satisfy 6−13≤b≤6+13,6 - 13 \le b \le 6 + 13\textsf{,} so −7≤b≤19.-7 \le b \le 19\textsf{.} The value 1111 is in this interval.

Practice playeasy

The midpoint of PQ‾\overline{PQ} is (6,2)(6, 2), and P=(9,8)P = (9, 8). What is the yy-coordinate of QQ?

Since 8+Qy2=2\dfrac{8 + Q_y}{2} = 2, we get Qy=4−8=−4Q_y = 4 - 8 = -4.

Practice playmedium

The equation of a line is y=12x−3y = \dfrac{1}{2}x - 3. Which equation represents the line that is perpendicular to this line and passes through the point (2,−1)(2, -1)?

Perpendicular lines have slopes that are negative reciprocals, so m=−2m = -2. Substitute (2,−1)(2, -1) into y=−2x+by = -2x + b: −1=−2(2)+b=−4+b-1 = -2(2) + b = -4 + b, so b=3b = 3. The equation is y=−2x+3.y = -2x + 3\textsf{.}

Practice playeasy

Line ww is defined by y=−13x+4y = -\dfrac{1}{3}x + 4. Line zz is perpendicular to line ww in the coordinate plane. What is the slope of line zz?

Perpendicular lines have slopes that are negative reciprocals. The slope of line ww is −13-\dfrac{1}{3}, so the slope of line zz is 3.3\textsf{.}

Practice playeasy

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

The endpoints share the same yy-coordinate, so the diameter is horizontal with length ∣18−2∣=16.|18 - 2| = 16\textsf{.} The radius is half the diameter, so r=162=8.r = \dfrac{16}{2} = 8\textsf{.}

Practice playmedium

The equation (x−4)2+(y−2)2=36(x - 4)^2 + (y - 2)^2 = 36 represents Circle A. Circle B is obtained by shifting Circle A left 55 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (4,2)(4, 2) and radius 66. Shifting left 55 moves the center to (−1,2)(-1, 2), so Circle B is (x+1)2+(y−2)2=36(x + 1)^2 + (y - 2)^2 = 36.

Practice playeasy

The hyperbola x216−y29=1\dfrac{x^{2}}{16} - \dfrac{y^{2}}{9} = 1 has a vertex on the positive x-axis. What is the x-coordinate of that vertex?

Set y=0y = 0: then x2=16x^{2} = 16, so the vertices are (±4,0)(\pm 4, 0) and the positive x-coordinate is 44.

Practice playeasy

A circle in the coordinate plane has equation (x−2)2+(y−7)2=36.(x - 2)^{2} + (y - 7)^{2} = 36\textsf{.} What is the measure of the diameter of the circle?

The radius measures 66 units, so the diameter measures 1212 units.

Keep practicing

Turn expressing geometric properties with equations into game time.

The Georgia Milestones placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSG.GPE.B.6HSG.GPE.A.1HSG.GPE.A.3
The same skills on other tests
ATLASDC CAPEMO MAPNJSLA
Source and test overview
All Georgia Milestones prepOfficial test source
Reporting categories

More Geometry domains

Similarity, Right Triangles, and TrigonometryStudents reason formally about similarity and trigonometric ratios in right triangles.8 QsPractice →