Mathematics

Coordinate Geometry and Graphs

59 Questions

Coordinate geometry involves plotting linear equations, analyzing graphical data, and understanding planar graphs using vertices, edges, and faces. These concepts are essential for calculating intersection points and interpreting graphical information. Such questions frequently appear in engineering, state, and civil services examinations.

Euler graph formulaLinear equation graphsGraph intersection pointsBar graphsLinear functionsTangent equations

Coordinate Geometry and Graphs Questions

Multiple choice maths tangents and intersecting chords other theorems related to circles touching circles angle made by a chord and a tangent

For what positive value(s) of K will the graph of the equation $2x + y = K$ be tangent to the graph of the equation $x^2+ y^2= 45$?

  1. 5

  2. 10

  3. 15

  4. 20

  5. 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
  • The radius of circle is $\sqrt{45} = 3\sqrt5$ , center of circle is $(0,0)$
  • For the equation to be tangent to circle , the distance from center of circle to given line must be equal to radius of circle
  • So we get $k/\sqrt5 = 3\sqrt5$ , which gives $k=15$
Multiple choice

What is a linear function?

  1. A function whose graph is a straight line

  2. A function whose graph is a parabola

  3. A function whose graph is a circle

  4. A function whose graph is a hyperbola
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A linear function is a function whose graph is a straight line.

Multiple choice

What is a quadratic function?

  1. A function whose graph is a straight line

  2. A function whose graph is a parabola

  3. A function whose graph is a circle

  4. A function whose graph is a hyperbola
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A quadratic function is a function whose graph is a parabola.

Multiple choice

What is a linear function?

  1. A function whose graph is a straight line

  2. A function whose equation is a linear equation

  3. A function whose rate of change is constant

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A linear function is a function whose graph is a straight line, whose equation is a linear equation, and whose rate of change is constant.

Multiple choice

What is a quadratic function?

  1. A function whose graph is a parabola

  2. A function whose equation is a quadratic equation

  3. A function whose rate of change is not constant

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A quadratic function is a function whose graph is a parabola, whose equation is a quadratic equation, and whose rate of change is not constant.

Multiple choice

What is an even function?

  1. A function whose graph is symmetric about the y-axis

  2. A function whose equation is even

  3. A function whose rate of change is even

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

An even function is a function whose graph is symmetric about the y-axis, whose equation is even, and whose rate of change is even.

Multiple choice

Euler's formula states that for a connected graph with v vertices and e edges, the following equation holds:

  1. v + e = 2

  2. v - e = 2

  3. v + e = f

  4. v - e = f
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Euler's formula states that for a connected graph with v vertices and e edges, the following equation holds: v + e = f, where f is the number of faces in the graph.

Multiple choice

Which of the following is an example of a graphical representation in mathematics?

  1. A graph of a function

  2. A table of values
  3. The equation \(y = mx + b\)

  4. A Venn diagram
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A graph of a function is an example of a graphical representation in mathematics because it uses a graph to represent mathematical ideas.

Multiple choice

Which of the following is an example of a mathematical model?

  1. The equation \(y = mx + b\)

  2. A graph of a function

  3. A table of values

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The equation (y = mx + b), a graph of a function, and a table of values are all examples of mathematical models.

Multiple choice

What is the significance of the slope of a line in a line graph?

  1. It indicates the direction of the trend

  2. It represents the rate of change

  3. It shows the relationship between the variables

  4. It determines the accuracy of the graph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The slope of a line in a line graph represents the rate of change of the dependent variable with respect to the independent variable.

Multiple choice

What is a graph?

  1. A diagram showing the relationship between two or more variables.

  2. A mathematical equation that describes a relationship between two or more variables.

  3. A table of data showing the values of two or more variables.

  4. A chart that shows the distribution of data.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A graph is a visual representation of the relationship between two or more variables. It is used to show how the variables are related to each other and to identify trends or patterns in the data.

Multiple choice

What is a line graph?

  1. A graph that shows the relationship between two variables using a line.

  2. A graph that shows the distribution of data using a line.

  3. A graph that shows the relationship between two variables using a bar.

  4. A graph that shows the distribution of data using a bar.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A line graph is a graph that shows the relationship between two variables using a line. The line is plotted on a coordinate plane, with the independent variable on the x-axis and the dependent variable on the y-axis.

Multiple choice

What is a bar graph?

  1. A graph that shows the relationship between two variables using a bar.

  2. A graph that shows the distribution of data using a bar.

  3. A graph that shows the relationship between two variables using a line.

  4. A graph that shows the distribution of data using a line.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A bar graph is a graph that shows the relationship between two variables using a bar. The bars are plotted on a coordinate plane, with the independent variable on the x-axis and the dependent variable on the y-axis.