MO MAP Geometry Expressing Geometric Properties with Equations Practice

Expressing Geometric Properties with Equations skills

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

Use coordinates to prove simple geometric theorems algebraically

Prove theorems involving lines and segments in the coordinate plane

Standards basis

Missouri Learning Standards (Mathematics K-5 and Mathematics 6-12; revised standards approved April 19, 2016) — Missouri

How the MO MAP reports it

Missouri’s MAP math is built from the Missouri Learning Standards and the state’s item specifications, not from a separate national testing framework. The standards are closely CCSS-aligned in structure, with grade-level and course-level domains used as the native reporting/coverage structure.

Blueprint & weighting

Missouri publishes grade-level and EOC blueprints, but the accessible official pages in this pass did not expose the domain-by-domain percentage tables. The assessment page states that item specifications organize expectations by domains/strands and that blueprints are available for grade-level and EOC assessments.

Official sources

Missouri Department of Elementary and Secondary Education — Missouri Learning Standards
Missouri Department of Elementary and Secondary Education — Mathematics
Missouri Department of Elementary and Secondary Education — Assessment

8 free questions · 0/0 correct

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 playmedium

The equation $x^2 + (y + 2)^2 = 16$ represents Circle A. Circle B is obtained by shifting Circle A down $5$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(0, -2)$ and radius $4$ . Shifting down $5$ moves the center to $(0, -7)$ , so Circle B is $x^2 + (y + 7)^2 = 16$ .

Practice playmedium

The graph of the equation $(x + 6)^2 + (y - 4)^2 = 100$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a\textsf{?}$

The center is $(-6, 4)$ and the radius is $10\textsf{.}$ A point on the circle must satisfy $-6 - 10 \le a \le -6 + 10\textsf{,}$ so $-16 \le a \le 4\textsf{.}$ The value $-11$ is in this interval.

Practice playeasy

The ellipse $\dfrac{x^{2}}{25} + \dfrac{y^{2}}{9} = 1$ crosses the positive x-axis at one point. What is the x-coordinate of that point?

Set $y = 0$ : then $x^{2} = 25$ , and the positive solution is $x = 5$ .

Practice playeasy

A circle in the coordinate plane has equation $(x - 1)^{2} + (y - 4)^{2} = 81\textsf{.}$ What is the value of $r^{2}\textsf{?}$

In standard form the right side equals $r^{2}\textsf{,}$ so $r^{2} = 81\textsf{.}$

Practice playeasy

$M(4, 7)$ is the midpoint of segment $AB$ , and $A = (1, 5)$ . What is the $x$ -coordinate of $B$ ?

Since $\dfrac{1 + B_x}{2} = 4$ , we get $B_x = 8 - 1 = 7$ .

Practice playmedium

The equation of a line is $y = \dfrac{1}{2}x - 4$ . Which equation represents the line that is parallel to this line and passes through the point $(6, 1)$ ?

Parallel lines have the same slope, so $m = \dfrac{1}{2}$ . Substitute $(6, 1)$ into $y = \dfrac{1}{2}x + b$ : $1 = \dfrac{1}{2}(6) + b = 3 + b$ , so $b = -2$ . The equation is $y = \dfrac{1}{2}x - 2\textsf{.}$

Practice playeasy

Line $t$ is defined by $y = 5x - 8$ . Line $k$ is perpendicular to line $t$ in the coordinate plane. What is the slope of line $k$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $t$ is $5$ , so the slope of line $k$ is $-\dfrac{1}{5}\textsf{.}$

MO MAP Geometry Expressing Geometric Properties with Equations. Practice it free.

Expressing Geometric Properties with Equations skills

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

Use coordinates to prove simple geometric theorems algebraically

Prove theorems involving lines and segments in the coordinate plane

Topics mapped to this domain

Circle diameter endpoints to radius (SAT)

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

Possible coordinates on a circle (SAT)

Conic sections

Equation of a circle

Midpoint formula

Parallel and perpendicular lines through a point (SAT)

Parallel and perpendicular slopes from slope-intercept form

8 free questions · 0/0 correct

Turn expressing geometric properties with equations into game time.

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