Important Questions for Class 10 Chapter 7 - Coordinate Geometry

The set of PDF of important questions will help you in doing a complete revision in Maths and getting good scores.

Important questions based on NCERT syllabus for Class 10 Chapter 7 - Coordinate Geometry:

Question 1: Find the area of a triangle whose vertices are A (3, 2), B (11, 8) and C(8, 12).
Solution:
Let A=(x1,y1)=(3,2),
B(x2,y2)=(11,8)
and C=(x3,y3)=(8,12) be the given points. Then,

Area of ΔABC=1/2|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|

Area of ΔABC = 1/2|3(8 − 12) + 11(12 − 2) + 8(2 − 8)|
Area of ΔABC = 1/2|−12 + 110 − 48| = 25 sq. units

Question 2: Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7).
Solution:
Suppose the line 3x + y -9 = 0 divides the line segment joining A(1, 3) and B(2, 7) in the ratio k:1 at point C.

Then, the coordinates of C are

((2k +1)/(k+1), (7k+3)/(k+1))
But, C lies on 3x + y -9 = 0. Therefore,
3(2k+1/k+1) + 1(7x+3/k+1) − 9 = 0
⇒ 6k + 3 + 7k + 3 − 9k − 9 = 0
⇒ k = 3/4
So, the required ratio is 3:4 internally.

Question 3: The coordinates of A, B, C are (6, 3), (–3, 5) and (4, – 2) respectively and P is any point (x, y). Show that the ratio of the areas of triangle PBC and ABC is | x+y−2/7|
Solution:
We have,
∴Area of ΔPBC=1/2|(5x+6+4y)−(−3y+20−2x)|
⇒Area of ΔPBC=1/2|5x+6+4y+3y−20+2x|
⇒Area of ΔPBC=1/2|7x+7y−14|
⇒Area of ΔPBC=7/2|x+y−2|
⇒Area of ΔABC=7/2|6+3−2|
[ Replacing x by 6 and y = 3 in Area of ΔPBC]

⇒ Area of ΔABC = 49/2
∴Area of ΔPBC Area of ΔABC = (7/2|x + y − 2|)/(49/2)
⇒ Area of ΔPBC Area of ΔABC = |x + y − 2| / 7