Master Coordinate Geometry: Enhance Your Math Education Skills

Question 1

Calculate the distance between the points (1, 2) and (5, 6).

Accepted Answer

10

Answer

2

Answer

5

Answer

15

Question 2

Identify the midpoint of the line segment joining the points (-3, 4) and (5, 2).

Accepted Answer

(1, 3)

Answer

(2, 6)

Answer

(4, 3)

Answer

(6, 2)

Question 3

Find the x-coordinate of the point of intersection of the lines y = 2x + 3 and y = x - 1.

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 4

Find the equation of the line that passes through the points (2, 5) and (4, 9).

Accepted Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = 2x - 1

Answer

y = x - 1

Question 5

Find the gradient of the line that has the equation y = 3x - 5.

Accepted Answer

3

Answer

-1

Answer

1

Answer

-3

Question 6

Which of the following points lies on the x-axis?

Accepted Answer

(2, 0)

Answer

(0, 3)

Answer

(1, 1)

Answer

(-3, 2)

Question 7

Which of the following points is located in the first quadrant of the Cartesian plane, where both x and y coordinates are positive?

Accepted Answer

(4, 2)

Answer

(-3, 4)

Answer

(2, -5)

Answer

(0, 0)

Question 8

Calculate the area of the triangle having vertices at the points (0, 0), (3, 0), and (0, 4).

Accepted Answer

6

Answer

12

Answer

24

Answer

48

Question 9

Classify the conic section represented by the equation: x^2 - 4y^2 = 16.

Accepted Answer

Hyperbola

Answer

Circle

Answer

Ellipse

Answer

Parabola

Question 10

Find the parametric equations for the line passing through the point (2, 3) and having a slope of -1/2.

Accepted Answer

x = 2 - t/2, y = 3 - t/2

Answer

x = 2 + t/2, y = 3 - t/2

Answer

x = 2 - t, y = 3 + t

Answer

x = 2 + t, y = 3 - t

Question 11

What is the equation of the circle centered at (2, -1) with a radius of 3 units?

Accepted Answer

(x - 2)² + (y + 1)² = 9

Answer

(x + 2)² + (y - 1)² = 9

Answer

(x - 2)² + (y + 1)² = 16

Answer

(x + 2)² + (y - 1)² = 16

Question 12

Are the points (1, 2), (3, 4), and (5, 6) collinear?

Accepted Answer

Yes

Answer

Insufficient information

Answer

No

Answer

None of the above

Question 13

Which equation represents a vertical line passing through the point (2, 3)?

Accepted Answer

x = 2

Answer

y = 3x

Answer

y = 2

Answer

x + y = 5

Question 14

What is the equation of the line that passes through the point (2, -1) and has a slope of 2?

Accepted Answer

y = 2x - 5

Answer

y = -2x + 5

Answer

y = 2x + 5

Answer

y = -2x - 5

Question 15

Calculate the distance between the points (-3, 5) and (2, 3).

Accepted Answer

√(34)

Answer

5√2

Answer

√(26)

Answer

10

Question 16

What are the coordinates of the vertex of the parabola represented by the equation y = x² - 4x + 3?

Accepted Answer

(2, -1)

Answer

(1, 2)

Answer

(-2, 1)

Answer

(-1, 2)

Question 17

What is the equation of the circle centered at (2, -1) with a radius of 3?

Accepted Answer

(x - 2)² + (y + 1)² = 9

Answer

(x + 2)² + (y - 1)² = 9

Answer

(x + 2)² + (y - 1)² = 3

Answer

(x - 2)² + (y + 1)² = 3

Question 18

Find the point of intersection of the lines y = 2x - 3 and y = -x + 5.

Accepted Answer

(2, 1)

Answer

(1, -2)

Answer

(-2, 1)

Answer

(1, 2)

Question 19

Which point is equidistant from the points (2, 3) and (-1, 1)?

Accepted Answer

(0, 2)

Answer

(2, 0)

Answer

(0, -2)

Answer

(1, 2)

Question 20

Calculate the area of the parallelogram with vertices (0, 0), (3, 2), (7, 2), and (4, 0).

Accepted Answer

6

Answer

9

Answer

3

Answer

12

Question 21

Which of the following transformations will map the point (2, -3) to the point (6, 3)?

Accepted Answer

Translation of 4 units to the right and 6 units up.

Answer

Translation of 6 units to the right and 4 units down.

Answer

Reflection about the x-axis followed by translation of 4 units to the right.

Question 22

Find the equation of the parabola with vertex at (-2, 3) and focus at (0, 3).

Accepted Answer

x = (y - 3)^2 - 2

Answer

x = -(y - 3)^2 - 2

Answer

x = (y + 3)^2 - 2

Answer

x = -(y + 3)^2 - 2