# 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=(x_{1},y_{1})=(3,2),

B(x_{2},y_{2})=(11,8)

and C=(x_{3},y_{3})=(8,12) be the given points. Then,

Area of ΔABC=1/2|x_{1}(y_{2}−y_{3})+x_{2}(y_{3}−y_{1})+x_{3}(y_{1}−y_{2})|

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