RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry Ex 16 A

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TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 16
Chapter NameCoordinate Geometry
Exercise16 A
CategoryRS Aggarwal Solutions

RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry Ex 16 A

Question 1:
(i) The given points are A(9,3) and B(15,11).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 1.1
(ii) The given points are A(7,4) and B(-5,1).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 1.2
(iii) The given points are A(-6, -4) and B(9,-12).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 1.3
(iv) The given points are A(1, -3) and B(4, -6).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 1.4
(v) The given points are P(a + b, a – b) and Q(a – b, a + b).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 1.5
(vi) The given points are P(a sin a, a cos a) and Q(a cos a, – a sina).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 1.6

Question 2:
(i) The given point is A(5, -12) and let O(0,0) be the origin.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 2.1
(ii) The given point is B(-5, 5) and let O(0,0) be the origin.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 2.2
(iii) The given point is C(-4, -6) and let O(0,0) be the origin.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 2.3

Question 3:
The given points are A(a, -1) and B(5,3).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 3.1

Question 4:
Let R(10,y) be the point at a distance of 10 units from P(2, -3).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 4.1

Question 5:
Let A(6, -1), B(1,3) and C(k,8) are the given points.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 5.1

Question 6:
Let A(a, 2), B(8, -2) and C(2,-2) be the given points. Then first we find:
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 6.1
Therefore, a = 5

Question 7:
Let any point P on x – axis is (x,0) which is equidistant from A(-2, 5) and B(-2, 9).
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 7.1
This is not admissible.
Hence, there is no point on x – axis which is equidistant from A(-2, 5) and B(-2, 9).

Question 8:
Let any point P on x – axis is (0,y) which is equidistant from A(5, -2) and B(-3, 2)
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 8.1
Thus, the point on y – axis is (0, -2).

Question 9:
he point A(4,3) and B(x,5) lie on a circle. Its centre is O(2,3)
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 9.1

Question 10:
Let A(6, -1) and B(2,3) be the given point and P(x,y) be the required point, we get
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 10.1

Question 11:
Let A(11, -8) be the given point and let P(x,0) be the required point on x – axis
Then,
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 11.1
Hence, the required points are (17,0) and (5,0).

Question 12:
Let the required points be P(x,y), then
PA = PB = PC. The points A, B, C are (5,3), (5, -5) and (1, -5) respectively.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 12.1
Hence, the point P is (3, -1).

Question 13:
Let A(1, -1), B(5, 2) and C(9, 5) are the given points. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 13.1
Hence the given points A, B, C are collinear.

Question 14:
(i) Let A (6,9), B(0,1) and C(-6, -7) be the given points. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 14.1
Hence the given A, B, C are collinear.
(ii) Let A(-1, -1), B(2,3) and C(8,11) be the given points. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 14.2
Hence the given A, B, C are collinear.
(iii) Let P(1,1), Q(-2,7) and R(3, -3) be the given points, then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 14.3
(iv) Let P(2,0), Q(11,6) and R(-4,-4) be the given points
Then,
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 14.4
Hence the given P, Q, R are collinear.

Question 15:
Let A(3,0), B(6,4) and C(-1,3) are the given points. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 15.1
∴ ∆ ABC is an isosceles right – angled triangle.
This shows that ∆ ABC is right angled at A.

Question 16:
Vertices of triangle ABC are A(7, 10), B(-2, 5) and C(3, -4)
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 16.1
∴ ∆ ABC is a right angled triangle.
Hence ∆ ABC is an isosceles right triangle.

Question 17:
Let A(-5,6), B(3,0) and C(9,8) be the given points. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 17.1

Question 18:
Let O(0,0), A(3,√3) and B(3,-√3) are the given points.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 18.1
Hence, DABC is equilateral and each of its sides being 2√3 units.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 18.2

Question 19:
Let A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram ABCD. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 19.1
Diagonal AC ≠ Diagonal BD.
Thus ABCD is not a rectangle but it is a parallelogram because its opposite sides are equal and diagonals are not equal.

Question 20:
(i) Let A(0, -4), B(6,2), C(3,5) and D(-3,-1) are the vertices of quad. ABCD. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 20.1
Thus, ABCD is a quadrilateral whose opposite sides are equal and the diagonals are equal.
Hence, quad. ABCD is a rectangle.
(ii) Let A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) be the angular points of quad. ABCD, then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 20.2
Thus, ABCD is a quadrilateral whose opposite sides are equal and diagonals are equal.
Hence, quad. ABCD is rectangle.
(iii) Let A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3) are the vertices of quad. ABCD. Then
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 20.3
Thus, ABCD is a quadrilateral whose opposite sides are equal and the diagonals are equal
Hence, quad. ABCD is a rectangle.

Question 21:
(i) Let A(6,2), B(2,1), C(1,5) and D(5,6) be the angular points of quad. ABCD. Join AC and BD
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 21.1
Thus, ABCD is a quadrilateral in which all sides are equal and the diagonals are equal.
Hence, quad ABCD is a square.
(ii) Let P(0, -2), Q(3,1), R(0,4) and S(-3,1) be the angular points of quad. ABCD
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 21.2
Thus, PQRS is a quadrilateral in which all sides are equal and the diagonals are equal.
Hence, quad. PQRS is a square.

(iii) The angular points of quadrilateral ABCD are A(3,2), B(0,5), C(-3,2) and D(0,-1)
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 21.3
Thus, all sides of quad. ABCD are equal and diagonals are also equal.
Quad. ABCD is a square.

Question 22:
Let A(-3,2), B(-5, -5), C(2, -3) and D(4,4) be the angular point of quad ABCD. Join AC and BD.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 22.1
Thus, ABCD is a quadrilateral having all sides equal but diagonals are unequal.
Hence, ABCD is a rhombus.
RS Aggarwal Solutions Class 10 Chapter 16 Co-ordinate Geometry 16a 22.2

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