Question

If the three points (5,1),(1,-1)and(p,4)are collinear,find the value of p​

Answer 1

Answer:

p = 11

Step-by-step explanation:

Given,

All the three points are collinear

A = (5 , 1)

B = (1 , -1)

C = (p , 4)

To Find :-

Value of 'p'

Formula Required :-

$Area=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

Solution :-

As the three points are collinear their area is zero.

• x_1 = 5 , y_1 = 1
• x_2 = 1 , y_2 = - 1
• x_3 = p , y_3 = 4

$0=\dfrac{1}{2}|5(-1-4)+1(4-1)+p(1-(-1))|$

0 = |5(-5) + 1(3) + p(2)|

0 = | -25 + 3 + 2p|

0 = -22 + 2p

2p = 22

p = 22/2

p = 11

∴ Value of 'p' = 11

Answer 2

Step-by-step explanation:

Given:If the three points (5,1),(1,-1) and (p,4)

To find:Value of p

Solution:

We know that if three points are collinear they can't form a triangle.

Thus,

Area of triangle formed by these points will be zero.

Area of triangle if vertices are given

$Area = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

Let A(5,1)

B(1,-1)

C(p,4)

Put the values in formula and equate to zero

$\frac{1}{2} \bigg (5( - 1 - 4) + 1(4 - 1) + p(1 - ( - 1)) \bigg) = 0 \\ \\ 5( - 5) + 1 \times 3 + 2p = 0 \\ \\ - 25 + 3 + 2p = 0 \\ \\ 2p = 22 \\ \\ p = \frac{22}{2} \\ \\ p = 11$

Value of p is 11 , if given points are collinear.

Final Answer:

p=11

Hope it helps you.

To learn more on brainly:

find the value of p for which the points (-5,1) , (1,p) , and (4,-2) are collinear.

https://brainly.in/question/1629806