Coordinate Geometry

Here are some essential Class 10 Mathematics questions for Chapter 7, Coordinate Geometry , carefully selected to assist students in preparing for the CBSE Class 10 Mathematics Examination in 2024-25. These thoughtfully curated questions cover various types of problems and aim to help students strengthen their problem-solving skills and gain a deeper understanding of the Coordinate Geometry chapter. By practicing this diverse range of questions, students can clarify any doubts they may have and improve their performance in this chapter.

Table of Contents

In this chapter, we will study concepts of coordinate geometry, graphs of linear equations, the distance formula, and the section formula for internal division.These concepts are essential in understanding the relationship between algebra and geometry.

Coordinate Geometry is a branch of mathematics that deals with the study of geometrical figures using a coordinate system. It involves representing points, lines, and shapes on a plane using ordered pairs of numbers (x, y) called coordinates.

(b) negative, positive

(c) negative, negative

(d) positive, positive

**Ans.**(b)

**Explanation:**

In the second quadrant, X-axis is negative and Y-axis is positive. Therefore, for a point the

abscissa is negative and the ordinate is positive.

(b) 4 : 7

(c) 7 : 4

(d) 4 : 5

**Ans.** (b)

**Explanation:**

Let, k : 1 be the ratio in which the X-axis divides the line joining (6,4) and (1,-7).

Let, P be the point on the X- axis that divides the line.

\text{Then} \space \space P(x,y)=\begin{pmatrix} \dfrac{k+6}{k+1},\dfrac{-7k+4}{k+1}\end{pmatrix} \\[4.5 bp]
\text{As P(x,y) lies on X-axis } \space P(x,0)=\begin{pmatrix} \dfrac{k+6}{k+1},\dfrac{-7k+4}{k+1} \end{pmatrix} \\[4.5 bp]
\text{[∵ x- coordinate will be (x,0)]} \\[4.5 bp]
\Rightarrow \dfrac{-7k+4}{k+1}=0 \\[4.5 bp]
⇒ -7k+4 = 0 \\[4.5 bp]
⇒ 7k=4 \\[4.5 bp]
\Rightarrow k= \dfrac{4}{7} \\[4.5 bp]
\text{So, the required ratio be} \space \space
k : 1 =\dfrac{4}{7}:1= 4 : 7

**Explanation:**

Let the coordinates of point A be (x,y) and point O (2,-3) be the center,

then,

\text{By mid-point formula,}\space\space\space\space\space\space\space\space \dfrac{x+1}{2}=\text{2 and }\dfrac{y+4}{2}=-3 \\[4.5 bp]
or x = 4 - 1 and y =- 6 - 4

\Rightarrow \space\space\space\space\space\space\space\space \text{x = 3 and y = - 10} \\[4.5 bp]

\therefore \space\space\space\space\space\space \text{The coordinates of point A are (3,- 10)}

**Explanation:**

Let the coordinates of point P be (2y, y). Since , P is equidistant from Q and R.

\therefore \space\space\space\space\space\space\space\space PQ = PR \\[4.5 bp]
\Rightarrow \space\space\space\space\space\space\space\space \sqrt{(2y-2)^2+(y+5)^2}=\sqrt{(2y+3)^2 + (y-6)^2}\\[4.5 bp]
\Rightarrow \space\space\space\space\space\space\space\space (2y-2)^2 + (y + 5)^2= (2y + 3)^2 + (y - 6)^2 \\[4.5 bp]
\Rightarrow \space\space\space\space\space\space\space\space 4y^2 + 4 - 8y + y^2 + 25 + 10y = 4y^2 + 9 + 12y + y^2 + 36 - 12y \\[4.5 bp]
\Rightarrow \space\space\space\space\space\space\space\space 2y + 29 = 45 \\[4.5 bp]
\Rightarrow \space\space\space\space\space\space\space\space 2y = 45 - 29 \\[4.5 bp]
\Rightarrow \space\space\space\space\space\space\space\space y=\dfrac{16}{2} = 8

Hence, the coordinates of point P are (16,8).

**Explanation:**

Given, A = (3, – 1), B = (8, 9) and x – y – 2 = 0

Let the line x – y – 2 = 0 intersect the line segment AB at R in the ratio p : 1.

Now, Rx = \dfrac{1(3)+p(8)}{p+1} \space \space and \space \space R_y =\dfrac{1(-1)+p(9)}{p+1} \\[4.5 bp] \Rightarrow \space\space R_x =\dfrac{3+8p}{p+1} \space\space and \space\space R_y =\dfrac{-1+9p}{p+1}\\[4.5 bp] \text{Thus,} \space \space R = \begin{pmatrix} \dfrac{3+8p}{p+1},\dfrac{9p-1}{p+1} \end{pmatrix} \\[4.5 bp]

Now substituting the value of R in the given equation,

\text{we get} \\[4.5 bp] \dfrac{3+8p}{p+1}-\dfrac{9p-1}{p+1}-2=0 \\[4.5 bp] \Rightarrow\space\space\space\space 3 + 8p – 9p + 1 – 2(p + 1) = 0 \\[4.5 bp] \Rightarrow\space\space\space\space 4 – p – 2p – 2 = 0 \\[4.5 bp] \Rightarrow\space\space\space\space 3p = 2 \\[4.5 bp] \Rightarrow\space\space\space\space P=\dfrac{2}{3}\\[4.5 bp] \text{Thus, the ratio is} \space \dfrac{2}{3} : 1 = 2 : 3.Chapter No. | Chapter Name |
---|---|

Chapter 1 | Real Numbers |

Chapter 2 | Polynomials |

Chapter 3 | Pair of Linear Equations in Two Variable |

Chapter 4 | Quadratic Equations |

Chapter 5 | Arithmetic Progressions |

Chapter 6 | Triangles |

Chapter 7 | Coordinate Geometry |

Chapter 8 | Introduction to Trigonometry |

Chapter 9 | Some Applications of Trigonometry |

Chapter 10 | Circles |

Chapter 11 | Areas Related to Circle |

Chapter 12 | Surface Areas and Volumes |

Chapter 13 | Statistics |

Chapter 14 | Probability |

To improve your understanding of the chapter’s concepts, oswal.io offers a wide range of practice questions. Their extensive question bank is designed to help you reinforce your knowledge and enhance your problem-solving skills. By using these resources, you can strengthen your grasp of the topics and become better at solving various types of problems.

Ans: Coordinate Geometry is a branch of mathematics that involves the study of geometric figures using coordinate systems. It relates algebraic equations to geometric shapes and positions them on a coordinate plane.

Ans: The coordinates of the origin are (0, 0). It is the point where the x-axis and y-axis intersect.

Ans: The distance between two points (x_1, y_1) and (x_2, y_2) on the coordinate plane can be calculated using the Distance Formula: Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]

Ans: The Section Formula for internal division gives the coordinates (x, y) of a point P that divides a line segment joining two points A(x₁, y₁) and B(x₂, y₂) in a given ratio ‘m:n’ internally as: x = [(mx₂ + nx₁)/(m + n)], y = [(my₂ + ny₁)/(m + n)]

Ans: The x-axis and y-axis are essential components of the coordinate plane. The x-axis represents the horizontal axis, and the y-axis represents the vertical axis. They intersect at the origin (0, 0). The coordinates of any point on the plane are determined by its position along these two axes.

Chapter Wise Important Questions for CBSE Board Class 10 Maths |
---|

Real Numbers |

Polynomials |

Pair of Linear Equations in Two Variables |

Quadratic Equations |

Arithmetic Progressions |

Triangles |

Coordinate Geometry |

Introduction to Trigonometry |

Some Applications of Trigonometry |

Circles |

Areas Related to Circles |

Surface Areas and Volumes |

Statistics |

Probability |

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