Question

22. If the point A (X,2) B(3,4) and C(7,8) are collinear. what is the value of x

plz... answer give the correct answer ​

Answer 1

Step-by-step explanation:

Given:-

The points A (X,2) B(3,4) and C(7,8) are collinear.

To find:-

What is the value of x ?

Solution:-

Given points are A (X,2) ,B(3,4) and C(7,8)

(x1, y1)=A (X,2)=>x1 = X and y1 = 2

(x2, y2)=B(3,4)=>x2 = 3 and y2 = 4

(x3, y3)=C(7,8)=>x3 = 7 and y3 = 8

Given that the points are collinear points.

We know that

The area of a triangle formed by the points (x1, y1),(x2, y2) and (x3, y3) is equal to zero then the they are collinear points.

Area of triangle =(1/2)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| sq.units

=>∆=0

=>(1/2)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| = 0

On Substituting the values in the above formula then

=>(1/2) | X(4-8)+3(8-2)+7(2-4) |= 0

=>(1/2) | X(-4)+3(6)+7(-2) | = 0

=>(1/2) | -4X+18-14 | = 0

=>(1/2) | -4X+4 | = 0

=>(-4X+4 )/2 = 0

=>(-4X+4)=0×2

=>-4X+4 = 0

=>-4X = -4

=>X = -4/-4

=>X = 1

Therefore, X = 1

Answer:-

The value of X for the given problem is 1

Used formulae:-

• The points lie on the same line are called collinear points.
• The area of a triangle formed by the points (x1, y1),(x2, y2) and (x3, y3) is equal to zero then the they are collinear points.

Area of triangle =(1/2)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| sq.units

Answer 2

Answer:

Question

❇️If the point A (X,2) B(3,4) and C(7,8) are collinear. what is the value of x

Solution

✍️Refer to the attachment ⬆️

<<------------------------------------------------->>

Extra information

• Answer will always be in positive sign . If it is negative then your answer is wrong

<<----------------------------------------------->>

Extra information

• To find collinear:x1(y2-y3)+x2(y2-y1)+x3(y1-y2)=0
• Distance formula:d(AB)=√(x2-x1)²+(y2-y1)²
• Section formula:
• $= = > x = \frac{mx2 + nx1}{m + n} \\ = = > y = \frac{my2 + ny1}{m + n}$
• Midpoint formula:
• $= = > x = \frac{x1 + x2}{2} \\ = = > y = \frac{y1 + y2}{2}$
• centroid formula:
• $= = > x = \frac{x1 + x2 + x3}{3} \\ = = > y = \frac{y1 + y2 + y3}{3}$

Step-by-step explanation:

hope you appreciate this ans