Samacheer Kalvi 10th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.1

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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.1

Question 1.
Find the area of the triangle formed by the points
(i) (1, -1), (-4, 6) and (-3, -5)
(ii) (-10, -4), (-8, -1) and (-3, -5)
Solution:

(ii) (-10, -4), (-8, -1) and (-3, -5)

Question 2.
Detemine whether the sets of points are collinear ?

Solution:
(i)


∴ The given points are collinear

Question 3.
Vertices of given triangles are taken in order and their areas are provided aside. In each case, find the value of ‘p’.

Solution:
Area 20 sq. units.

8p = 104
p = 13

Question 4.
In each of the following, find the value of ‘a’ for which the given points are collinear.
(i) (2, 3), (4, a) and (6, -3)
(ii) (a, 2 – 2a), (-a + 1, 2a) and(-4 – a,6 – 2a)
Solution:

Question 5.
Find the area of the quadrilateral whose vertices are at
(i) (-9, -2), (-8, -4), (2, 2) and (1, -3)
(ii) (-9, 0), (-8, 6), (-1, -2) and (-6, -3)
Solution:
(i) (-9, -2), (-8, -4), (2, 2), and (1, -3)

(ii) (-9, 0), (-8, 6), (-1, -2) and (-6, -3)

Question 6.
Find the value of k, if the area ofa quadrilateral is 28 sq.units, whose vertices are (-4, -2), (-3, k), (3, -2) and (2, 3)
Solution:

Question 7.
If the points A(-3, 9) , B(a, b) and C(4,-5) are collinear and if a + b = 1, then find a and b.
Solution:

Question 8.
Let P(11, 7), Q(13.5, 4) and R(9.5, 4) be the mid-points of the sides AB, BC and AC respectively of ∆ABC . Find the coordinates of the vertices A, B and C. Hence find the area of ∆ABC and compare this with area of ∆PQR.
Solution:
p (11, 7), Q (13.5, 4), and R (9.5, 4) are the mid points of the sides of a ∆ABC.

Question 9.
In the figure, the quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of the patio.

Solution:
Area of the patio = Area of the quadrilateral ABCD – Area of the swimming pool EFGFI.
Area of the quadrilateral ABCD

Question 10.
A triangular shaped glass with vertices at A(-5, -4), B(1, 6) and C(7, -4) has to be painted.
If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied.
Solution:

Question 11.
In the figure, find the area of
(i) triangle AGF
(ii) triangle FED
(iii) quadrilateral BCEG
Solution: