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Quizzes > High School Quizzes > Mathematics

Coordinate Geometry Post Test Practice Quiz

Ace your post test with focused geometry review

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art promoting Coordinate Conquest, a high school geometry quiz game.

This coordinate geometry quiz helps you check Grade 9 skills like points, slope, distance, midpoint, equations of lines, and graphs in 20 quick questions. Use it as a post test to spot gaps before an exam and know what to review next.

In which quadrant does the point (-3, 4) lie?
Quadrant I
Quadrant IV
Quadrant III
Quadrant II
The point (-3, 4) has a negative x-coordinate and a positive y-coordinate, which places it in Quadrant II. This is because points in Quadrant II always have x-values less than zero and y-values greater than zero.
What are the coordinates of the origin in the coordinate plane?
(-1, 0)
(0, 0)
(1, 1)
(0, -1)
The origin is the point where the x-axis and y-axis intersect, which is at (0, 0). It serves as the central reference point in the coordinate plane.
What is the slope of a horizontal line?
1
No slope
Undefined
0
A horizontal line has no vertical change, therefore its rise is zero, resulting in a slope of 0. This is calculated using the formula rise over run.
What is the slope of a vertical line?
Infinite
0
1
Undefined
A vertical line has no horizontal change, which leads to a division by zero when using the slope formula, resulting in an undefined slope. Thus, the slope cannot be expressed as a real number.
On the coordinate plane, the x-coordinate indicates movement along which axis?
Neither axis
Diagonal axis
Vertical axis
Horizontal axis
The x-coordinate measures horizontal displacement on the coordinate plane. It indicates movement along the horizontal axis, which is fundamental in understanding coordinate geometry.
What is the midpoint of the segment connecting the points (2, 3) and (8, 7)?
(4, 5)
(6, 5)
(5, 5)
(5, 6)
The midpoint is calculated by averaging the x-coordinates and y-coordinates separately: ((2+8)/2, (3+7)/2) = (5, 5). This point is exactly in the middle of the two endpoints.
Using the distance formula, what is the distance between the points (1, -2) and (4, 2)?
7
5
6
5.5
The distance formula is sqrt((x2-x1)² + (y2-y1)²). Substituting the points gives sqrt((4-1)² + (2-(-2))²) = sqrt(9+16) = sqrt(25) = 5. This is the correct distance.
What is the slope of the line passing through the points (1, 2) and (3, 8)?
4
1
3
2
The slope is calculated as (y2 - y1) / (x2 - x1), so (8-2)/(3-1) equals 6/2, which simplifies to 3. This represents the steepness of the line.
Which equation represents a line with a slope of 2 and a y-intercept of -3?
y = 2x + 3
y = 2x - 3
y = -2x - 3
y = -2x + 3
In slope-intercept form, y = mx + b, the slope (m) is 2 and the y-intercept (b) is -3. The equation y = 2x - 3 correctly represents these values.
What is the x-intercept of the line given by the equation 2x + 3y = 6?
(3, 0)
(0, 3)
(0, 2)
(2, 0)
To find the x-intercept, set y to zero in the equation: 2x = 6, which gives x = 3. Thus, the x-intercept is at the point (3, 0).
If a line is perpendicular to a line with a slope of 1/2, what is the slope of the perpendicular line?
-2
2
1/2
-1/2
Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 1/2 is -2, making it the correct answer.
Which point lies on the line y = -3x + 6?
(1, 3)
(2, 0)
(0, 6)
(-1, 9)
Substituting x = 1 into the equation gives y = -3(1) + 6, which simplifies to 3. Hence, the point (1, 3) lies on the line.
Find the equation of the line that passes through (2, -1) with a slope of 4.
y = 4x + 9
y = 4x - 7
y = 4x - 9
y = 4x + 7
Using the point-slope form, y + 1 = 4(x - 2) simplifies to y = 4x - 8 - 1, which results in y = 4x - 9. This is the equation of the desired line.
What is the point that is symmetric to (5, -3) with respect to the origin?
(3, -5)
(-5, -3)
(-5, 3)
(5, 3)
Reflecting a point through the origin means reversing the sign of both coordinates. Thus, (5, -3) becomes (-5, 3), which is the correct symmetric point.
When the point (4, 2) is rotated 90° counterclockwise about the origin, what are its new coordinates?
(4, -2)
(-2, 4)
(2, -4)
(-4, -2)
A 90° counterclockwise rotation of a point (x, y) results in (-y, x). Applying this gives (-2, 4) from the point (4, 2).
Are the points (1, 2), (3, 6), and (5, 10) collinear?
No, they form a triangle
Yes, they are collinear
They are parallel
They are perpendicular
To determine collinearity, we compare the slopes between pairs of points. Since the slope from (1, 2) to (3, 6) and from (3, 6) to (5, 10) are both 2, the points lie on the same straight line.
What is the area of the triangle formed by the vertices (0, 0), (4, 0), and (4, 3)?
7
6
12
8
The area of a right triangle is given by 1/2 times the product of the base and height. With a base of 4 and a height of 3, the area is 1/2 * 4 * 3 = 6.
For the circle with equation (x - 2)² + (y + 1)² = 16, what is its center and radius?
Center (2, -1) and radius 16
Center (2, 1) and radius 4
Center (-2, 1) and radius 4
Center (2, -1) and radius 4
The standard form of a circle's equation is (x - h)² + (y - k)² = r². Comparing, we see that h = 2, k = -1, and r² = 16, so the radius r is 4.
What is the equation of the line parallel to y = -2x + 5 that passes through (-1, 3)?
y = -2x - 1
y = -2x + 1
y = 2x - 1
y = 2x + 1
Parallel lines share the same slope. Since the given line has a slope of -2, the new line must also have a slope of -2. Using the point (-1, 3) in the point-slope form yields y = -2x + 1.
Given that the midpoint of a segment is (3, -2) and one endpoint is (1, 4), what is the coordinate of the other endpoint?
(-5, -8)
(5, -8)
(-5, 8)
(5, 8)
Using the midpoint formula, the other endpoint can be found by doubling the midpoint coordinates and subtracting the known endpoint's coordinates. This calculation results in (5, -8) as the other endpoint.
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Study Outcomes

  1. Analyze coordinate plane relationships by identifying points, lines, and key geometric features.
  2. Apply distance and midpoint formulas to solve coordinate geometry problems.
  3. Graph linear equations and interpret their intersections within the coordinate plane.
  4. Determine slopes of lines to evaluate parallelism and perpendicularity.
  5. Synthesize algebraic and geometric concepts to solve real-world coordinate problems.

Post Test: Coordinate Geometry Cheat Sheet

  1. Understanding the Cartesian Coordinate System - Imagine playing a video game on a giant grid where every location has an address! The x‑axis and y‑axis cross at the origin (0,0) and carve the plane into four colorful quadrants, each with its own vibe. Get comfortable with this setup and you'll be teleporting around graphs in no time.
  2. Mastering the Distance Formula - Think of the distance formula as your built‑in GPS: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) tells you the straight‑line path between two points. No more zigzagging guesses - this trusty equation gives you the exact route every time.
  3. Learning the Midpoint Formula - Want the halfway chill spot between two coordinates? Use \(M(x, y) = \bigl(\frac{x_1 + x_2}, \frac{y_1 + y_2}\bigr)\) to pin it down. It's like finding the sweet center of a sandwich - perfectly balanced!
  4. Grasping the Slope Formula - How steep is your ride? With \(m = \frac{y_2 - y_1}{x_2 - x_1}\), you measure the incline or decline between any two points. It's the ultimate slope detector for hills, ramps, and trend lines alike.
  5. Equation of a Line in Slope‑Intercept Form - The classic \(y = mx + c\) is like the rulebook of line behavior: \(m\) is your slope coach and \(c\) is your starting play at the y‑intercept. Once you crack this code, you'll graph lines faster than you can say "coordinate geometry."
  6. Using the Section Formula - Slice a segment into any ratio you like! \(P(x,y)=\bigl(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\bigr)\) helps you mark exactly where to split, whether it's 2:1 or 7:3. It's your precision pizza cutter on the coordinate plane.
  7. Calculating the Area of a Triangle - Turn vertices into area with \(\frac\bigl|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\bigr|\). It's like a secret recipe that blends three points into a single number - triangle magic!
  8. Identifying Parallel & Perpendicular Lines - Parallel lines share the same slope (\(m_1=m_2\)), so they never say "hello." Perpendicular lines are more dramatic: their slopes multiply to - 1 (\(m_1\times m_2=-1\)), making a perfect right angle. Know these pairs and you'll spot relationships at a glance.
  9. Converting the General Form of a Line - The formal \(Ax+By+C=0\) is your tuxedo suit for lines. Flip it into \(y=mx+c\) by isolating \(y\) and dividing by \(B\), then you're ready to graph or analyze slope and intercept in style.
  10. Practicing Plotting & Graphing - Theory is cool, but nothing beats sketching points and drawing lines yourself. Grab graph paper or a digital tool, plot those coordinates, and watch patterns pop - practice turns concepts into second nature!
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