Sectional Formula MCQ Quiz in मल्याळम - Objective Question with Answer for Sectional Formula - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

CONCEPT:

Let A (x1, y1) and B (x2, y2) be the two given points and the point P (x, y) divide the line joining the points A and B in the ratio m : n, then

• Point of internal division is given as: 
• Point of external division is given as: 

Note: If P is the mid-point of line segment AB, then 

CALCULATION:

Let y -axis divides the line joining the points A(- 4, 2) and B(8, 3) in the ratio m : 1.

Let C be the point of intersection.

As we know that, the point  internal division is given by: 

C is the point of division i.e C lies on the y-axis and equation of y-axis is x = 0.

So, the point C will satisfy the equation x = 0

⇒ 8m - 4 = 0

⇒ m = 1/2

So, the required ratio is (1/2) : 1 = 1 : 2

Hence, option A is the correct answer.

Concept:

Let A = (x1 ,y1) and B = (x2 ,y2) be any two-point. let P (x,y) be any point on AB and 

By section formula we have, 

 and 

Calculations:

Given, the line y = 0 divides the line joining the points (3, -5) and (-4, 7).

consider, the line y = 0 divides the line joining the points (3, -5) and (-4, 7) at point P(x, y) in the ratio .

Now find the value of 

A = (3 ,5) = (x₁ ,y₁) and B = (- 4, 7) = (x2 ,y₂) 

By section formula we have, 

 and 

Consider, 

⇒

⇒ 

⇒ 

Hence, the line y = 0 divides the line joining the points (3, -5) and (-4, 7) at point P(x, y) in the ratio  i.e. 7 : 5

Given:

m : n = K : 1

If the point P divides the line segment AB internally in the ratio K ∶ 1 

Concepts used: 

P(x, y) = 

Calculation:

In the above given formula:

m : n = K : 1

Replacing the given values in the above formula:

P(x, y) = 

The answer is None of these.

Given

Concept:

In any straight line AB, whose coordinates are A(x1, y1) and B(x₂, y₂) and if the mid-point of AB is C(x, y), then,

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

Solution

Let us assume the coordinate of A as (x, y).

⇒ x = (x1 + x2)/2

⇒ 2 = (x1 + 1)/2

⇒ x = 4 - 1 = 3

Similarly, y will be:

⇒ y = (y1 + y2)/2

⇒ - 3 = (y1 + 4)/2

⇒ y = - 6 - 4

⇒ y = - 10

Hence, we get the coordinates of A as (3, -10).

Given

The coordinates are: 

A (-3, 10) and B (6, -8) 

Concept used

Using the section formula, if a point (x, y) divides the line joining the points x₁, y₁ and x₂, y₂ in the ratio m: n, then

(x, y) = (mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)

Solution

Let the ratio be m: n, then

⇒ (mx2 + nx1)/(m + n) = - 1

⇒ (6m - 3n)/(m + n) = - 1

⇒ (6m - 3n) = - m - n

⇒ 7m = 2n

⇒ m: n = 2: 7

Now,

(my2 + ny1)/(m + n) = y

⇒ (- 8 × 2 + 10 × 7)/(2 + 7) = y 

⇒ - 16 + 70 = 9y

⇒ 9y = 54

⇒ y =  6

Hence, The correct option is 4

Concept:

Let A = (x1 ,y1) and B = (x2 ,y2) be any two-point. let P (x,y) be any point on AB and 

By section formula we have, 

 and 

Calculations:

Given, the line y = 0 divides the line joining the points (3, -5) and (-4, 7).

consider, the line y = 0 divides the line joining the points (3, -5) and (-4, 7) at point P(x, y) in the ratio .

Now find the value of 

A = (3 ,-5) = (x₁ ,y₁) and B = (- 4, 7) = (x2 ,y₂) 

By section formula we have, 

 and 

Consider, 

⇒

⇒ 

⇒ 

Hence, the line y = 0 divides the line joining the points (3, -5) and (-4, 7) at point P(x, y) in the ratio  i.e. 5 : 7

Concept:

Section formula is used to find the ratio in which a line segment is divided by a point internally or externally. According to this formula, if a point P (lying on AB) divides AB in the ratio m : n then,

      ----(1)

Calculation:

Given that m : n = 2 : 3 and points are (8, 9) and (-7, 4)

Using equation (1), we get,

⇒ P = (2, 7)

Hence, The coordinates of the point which divides the line segment joining the points (8, 9) and (-7, 4) internally in the ratio 2 ∶ 3 are (2, 7).

Concept:

Internal Section Formula: 

Let A and B be the given two points (x1, y1) and (x2, y2) respectively and

P(x, y) be the point dividing the line segment AB internally in the ratio

m : n then 

⇔ P (x, y) = 

Calculation:

By using the above concept

x = 

y = 

Since, R(x, y) also lies on the line x + y = 4. Therefore,

⇒ 12k = 4(k + 1)

⇒ 12k - 4k = 4

⇒ 8k = 4

⇒ k = 4/8 = 1/2

Hence, the required ratio is PR ∶ RQ = 1 : 2

Concept:

Let A(x1, y1) and B(x2, y2) be the two points then the mid-point of the line joining the points A and B is 

Calculation:

Given: C(3, - 4) and D(- 1, 6)

As we know that, the mid-point of the line joining the points A(x1, y1) and B(x2, y2) is given by 

Let R be the mid-point between the points C and D.

Hence, the correct option is 1.

Concept:

If a point P divides a line joining points A(x1, y1) and B(x2, y2) in a ratio of m:n, then

,  and 

Calculation:

Given point are (1, 2) and (3, 0)

Midpoint divides the line in ratio 1 : 1

Let the mid-point be (x, y)

x = 

⇒ x = 

⇒ x =  = 2

Similarly 

y = 

⇒ y = 

⇒ y =  = 1

∴ The mid-point is (2, 1)