Page 46 - Mathematics Class - X

8. Using section formula, find the coordinates of C.

9. Coordinates of C obtained from Step 7 and Step 8 are the same.

OBSERVATIONS

1. Coordinates of A are ____________ .

2. Coordinates of B are ____________ .
3. Point C divides AB in the ratio ____________ .

4. Coordinates of C from the graph paper are ____________ .
5. Coordinates of C by using section formula are ____________ .

6. Coordinates of C from the graph paper and from section formula are ____________ .

INFERENCE
Section formula is obtained.

EXTENDED TASK
Find the coordinates of a point which divides the line segment in the ratio 2 : 3.

APPLICATION
This formula is used to find the centroid of a triangle in geometry, vector algebra and 3-dimensional geometry.

Viva-Voce

1. What is co-ordinate geometry?

Ans. The use of algebra to study geometric properties is called coordinate geometry. It operates on symbols
defined in a coordinate system.
2. Write the distance formula for the points A (x, y) and B (x , y )?
1
1
Ans. AB = (x − 1 ) x 2 + (y − 1 ) y 2

3. How many quadrants are there in a Cartesian plane?

Ans. Four

4. Find the coordinates of midpoint of a line whose end points are P (x , y ) and Q (x , y ).
1 1 2 2
Ans. (x + x )/2 and (y + y )/2
1 2 1 2
5. If three vertices of a triangle are known, how will you find the type of triangle using this information?

Ans. By finding the distance between the three vertices using distance formula.

6. What are the coordinates of the mid-point of the line segment joining the points A (x , y ) and B (0, 0)?
1 1
x + 0 x y + 0 y
Ans. x = 1 = 1 ; y = 1 = 1
2 2 2 2

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