Mathematics

Coordinate Geometry and Graphs

77 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 constructions mid-point formula midpoints division of a line segment

Let ${P} _{1}$ and ${P} _{2}$ be two fixed points in $xy-plane$. A line ${L} _{1}=0$ passes through ${P} _{1}$ intersects $y-axis$ at $B$ and the line ${L} _{2}=0$ passes through ${P} _{2}$ and intersects $x-axis$ at $A$. If ${L} _{1}=0$ and ${L} _{2}=0$ are perpendicular then the locus of mid-point of$AB$ is

  1. $Straight line$
  2. $Circle$
  3. $Ellipse$
  4. $Parabola$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The locus of the midpoint of a segment whose endpoints move on axes while the lines are perpendicular results in a straight line relationship based on the fixed points P1 and P2.

Multiple choice maths average arithmetic mean of ap introduction to averages means

A line is such that the algebraic sum of the perpendicular on it from a number of point is zero. The line always passes through a fixed point that is 

  1. A. M of the given points

  2. GM of the given points

  3. HM of the given points

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The algebraic sum of perpendiculars from points (xi, yi) to a line ax + by + c = 0 being zero implies the line passes through the centroid (mean of x, mean of y).

Multiple choice maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

A line passes through the variable point $A(\lambda +1,2\lambda)$ meets the lines $7x+y-16=0,\ 5x-y-8=0,\ x-5y+8=0$ at $b,c,d$ respectively. Then $AC, AB, AD$ are in

  1. A.P

  2. G.P

  3. H.P

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By calculating the distances from A to the lines, one can show that the segments form an arithmetic progression based on the properties of the lines and the point A.

Multiple choice maths geometry similarity and right angled triangle angle theorems for a right angled triangle apollonius's theorem

Let $\Delta _1$ denotes the area of the triangle formed by the vertices $(a^3m^3 _1, am _1), (a^3m^3 _2am _2), (a^3m^3 _3, am _3)$ and $\Delta _2$ denotes the area of the triangle formed by the vertices $(2am _1m _2, a^2(m^2 _1+m^2 _2))$, $(2am _2m _3, a^2(m^2 _2+m^2 _3))$ and $(2am _3m _1, a^2(m^2 _3+m^2 _1))$. Then $\dfrac{\Delta _1}{\Delta _2}(a > 0)$ equals?

  1. $\dfrac{a}{2}$
  2. $2a$
  3. $\dfrac{a^3}{8}$
  4. $8a^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculating the area of the triangles using the determinant formula for coordinates and simplifying the ratio yields a/2.

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.