Coordinate Geometry in the (x, y) Plane

Test your understanding of points, lines, slopes, distances, midpoints, and equations in the Cartesian plane. This quiz covers the fundamentals of coordinate geometry and helps strengthen your skills in plotting, interpreting, and solving problems involving the (x, y) coordinate system.

1 / 30

The slope of the line passing through points (2, 3) and (5, 9) is:

2

- 2

\frac{1}{2}

- \frac{1}{2}

2 / 30

The equation of the line with slope 3 and y-intercept -2 is:

y = - 2 x + 3

y = 3 x + 2

y = 3 x - 2

y = - 2 x - 3

3 / 30

The distance between points (1, 2) and (4, 6) is:

6

5

\sqrt{13}

\sqrt{29}

4 / 30

The midpoint of the segment joining (-1, 4) and (5, 8) is:

(3, 6)

(4, 12)

(6, 2)

(2, 6)

5 / 30

The equation of the line parallel to y=2x+1 passing through (3,7) is:

y = 2 x + 1

y = 2 x + 13

y = 2 x - 1

y = - 2 x + 1

6 / 30

The x-intercept of the line 3x – 4y = 12 is:

- 4

3

4

- 3

7 / 30

The slope of the line perpendicular to y=-⅓x+5 is:

- \frac{1}{3}

- 3

3

\frac{1}{3}

8 / 30

The line y=-2x+1 is parallel to:

y = \frac{1}{2} x + 1

y = 2 x - 3

y = x + 1

y = - 2 x + 5

9 / 30

The equation of the vertical line passing through (4,-3) is:

x = 4

y = - 3

x = - 3

y = 4

10 / 30

The angle of inclination (in degrees) of a line with slope 1 is:

3 0^{\circ}

6 0^{\circ}

4 5^{\circ}

9 0^{\circ}

11 / 30

Two lines are parallel if their slopes are:

Negative reciprocals

Zero

Undefined

Equal

12 / 30

The line perpendicular to y=⅖x+1 has slope:

- \frac{5}{2}

\frac{5}{2}

\frac{2}{5}

- \frac{2}{5}

13 / 30

The equation of the line perpendicular to y=-3x+2 passing through (1,4) is:

y = - 3 x + 7

y = \frac{1}{3} x + \frac{11}{3}

y = \frac{1}{3} x - \frac{11}{3}

y = 3 x + 1

14 / 30

The lines 4x – 2y = 6 and 2x – y = 3 are:

Parallel

Perpendicular

Coincident

Intersecting but not perpendicular

15 / 30

The shortest distance from the point (2,3) to the line y=2x+1 is:

\sqrt{5}

5

\frac{5 \sqrt{5}}{3}

\frac{3 \sqrt{5}}{5}

16 / 30

The angle between the lines y=x and y=√3x is:

1 5^{\circ}

3 0^{\circ}

4 5^{\circ}

6 0^{\circ}

17 / 30

The condition for two lines a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 to be parallel is:

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

a_{1} a_{2} + b_{1} b_{2} = 0

a_{1} b_{2} = a_{2} b_{1}

18 / 30

The lines y=3x+2 and y=3x-4 are:

Parallel

Perpendicular

Coincident

Intersecting at (3,11)

19 / 30

The line perpendicular to x+y=7 and passing through (1,1) is:

x + y = 2

y = x + 7

x - y = 0

y = - x + 2

20 / 30

The distance between the parallel lines 3x+4y=6 and 3x+4y=12 is:

\frac{12}{5}

6

3

\frac{6}{5}

21 / 30

The slope of the tangent to the curve y=x² at x=2 is:

2

4

0

- 2

22 / 30

The equation of the tangent to y=x³ at (1,1) is:

y = 3 x - 2

y = x

y = - 3 x + 4

y = 2 x - 1

23 / 30

The normal line to y=√x at x=4 is:

y = 4 x - 18

y = \frac{1}{4} x + \frac{1}{2}

y = - 4 x + 18

y = - \frac{1}{4} x + 3

24 / 30

The condition for a line to be tangent to a circle is that the distance from the center equals the:

Radius

Diameter

Chord length

Circumference

25 / 30

The tangent to y=eˣ at x=0 has the equation:

y = - x + 1

y = e^{x}

y = 1

y = x + 1

26 / 30

The normal to the parabola y²=4x at (1,2) has slope:

1

- 1

2

- 2

27 / 30

The tangent to y=lnx at x=1 is:

y = x - 1

y = - x + 1

y = x

y = - x

28 / 30

The number of tangents from (2,3) to the circle x²+y²=9 is:

1

0

2

Infinite

29 / 30

The angle between the tangent and normal to a curve at a point is always:

9 0^{\circ}

0^{\circ}

4 5^{\circ}

18 0^{\circ}

30 / 30

The tangent to y=sinx at x=π has slope:

1

0

Undefined

- 1

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