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NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4

December 26, 2018 by Dattu

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 7 Coordinate Geometry Class 10 NCERT Solutions Ex 7.4.

  • Coordinate Geometry Class 10 Ex 7.1
  • Coordinate Geometry Class 10 Ex 7.2
  • Coordinate Geometry Class 10 Ex 7.3
BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 7
Chapter NameCoordinate Geometry
ExerciseEx 7.4
Number of Questions Solved8
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4

NCERT Solutions for Class 10 Maths

Question 1.Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).

Solution:
If the ratio in which P divides AB is k : 1, then the coordinates of the point P will be
\(\frac { k{ x }_{ 2 }+{ x }_{ 1 } }{ k+1 } ,\frac { k{ y }_{ 2 }+{ y }_{ 1 } }{ k+1 } \)
Let the given line divides the line segment joining the points A (2, – 2) and B (3, 7) in a ratio k: 1.
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 37

Question 2. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

Solution:
If the given points are collinear the area of triangle formed by these points will be O.
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 38

Question 3. Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3).

Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 39
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 40

Question 4. Find two opposite vertices of a square are (—1, 2) and (3, 2), find the coordinates of the other two vertices.

Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 41
Let ABCD be a square having (—1, 2), (3, 2) as vertices A and C respectively and (x, y), (x1, y1) be the coordinate of vertex B and D respectively.
We know that are sides of a square are equal to each other AB = BC
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 42
We know that in a square diagonals are of equal length and bisect each other at 900 Let O be the mid point of AC so it will also be the mid point of BD.
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 43

Question 5. The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a
triangular grassy lawn in the plot as shown in the Figure the students are to sow seeds of flowering plants on the remaining area of the plot.
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 44
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of ∆PQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?

Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 45

Question 6. The vertices of a MBC are A (4, 6), B (1, 5) and C (7, 2), A line is drawn to intersect sides AB and AC at D and E respectively, such that \(\frac { AD }{ AB } =\frac { AE }{ AC } =\frac { 1 }{ 4 } \)
Calculate the area of the ∆ADE and compare it with the area of ∆ABC.

Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 46
Coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2,y2) intenally in the ratio m1 : m2, are
\(\frac { { m }_{ 1 }{ x }_{ 2 }+{ m }_{ 2 }{ x }_{ 1 } }{ { m }_{ 1 }+{ m }_{ 2 } } ,\frac { { m }_{ 1 }{ y }_{ 2 }+{ m }_{ 2 }{ y }_{ 1 } }{ { m }_{ 1 }+{ m }_{ 2 } } \)
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 47

Question 7. Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of ∆ABC.
(i) The median from A meets BC at D. Find the coordinates of point D.
(ii) Find the coordinates of the point P on AD such that AP: PD = 2: 1
(iii) Find the coordinates of point Q and R on medians BE and CF respectively.
Such that BQ: QE = 2:1 and CR: RF = 2:1,
(iv) What do you observe?
(v) If A(x1, y1), B(x2, y2), and C(x3, y3) are the vertices of ∆BC, find the coordinates of the centroid of the triangle.

Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 48
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 49
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 50
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 51

Note: Coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2,y2) intenally in the ratio m1 : m2, are
\(\frac { { m }_{ 1 }{ x }_{ 2 }+{ m }_{ 2 }{ x }_{ 1 } }{ { m }_{ 1 }+{ m }_{ 2 } } ,\frac { { m }_{ 1 }{ y }_{ 2 }+{ m }_{ 2 }{ y }_{ 1 } }{ { m }_{ 1 }+{ m }_{ 2 } } \)

Question 8. ABCD is a rectangle formed by the points A (-1,-1), B (—1 4), C (5, 4) and D (5,—1). P, Q, R and S are the mid-points of AB, BC, CD, and DA respectively. Is the quadrilateral PQRS ¡s a square? a rectangle? Or a rhombus? Justify your answer.

Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 52
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 53
Here all sides of given quadrilateral is of same measure but the diagonals are of different lengths. So, PQRS is a rhombus.

We hope the NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4, drop a comment below and we will get back to you at the earliest.

Filed Under: CBSE Tagged With: NCERT Solutions for Class 10 Maths

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