Question

The points (2,1),(8,5)and (k,7) lie on a straight line. Then the values of k is

Answer 1

Step-by-step explanation:

Given -

• Points A(2,1), B(8,5), C(k,7) lies on a straight line

To Find -

• Value of k

As we know that :-

x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) = 0

Now,

A(2,1) = (x1,y1)

B(8,5) = (x2,y2)

C(k,7) = (x3, y3)

Then,

→ 2(5-7) + 8(7-1) + k(1-5) = 0

→ 2×(-2) + 8×(6) + k×(-4) = 0

→ -4 + 48 - 4k = 0

→ 4k = 44

→ k = 44/4

→ k = 11

Hence,

The value of k is 11.

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\large\underline\mathrm{The \: value \: of \: k \: is \: 11.}$

$\large\underline\mathrm{Given:-}$

• point A(2, 1), B(8, 5), C(k, 7) lies on a straight line.

$\large\underline\mathrm{To \: find}$

• Value of k ?

$\large\underline\mathrm{Using \: the \: formula}$

• x1(y2 - y3) + x3(y1 - y2) + x3(y1 - y3) = 0

$\large\underline\mathrm{Now}$

$\implies$ x1 = 2

$\implies$ y1 = 1

$\implies$ x2 = 8

$\implies$ y2 = 5

$\implies$ x3 = k

$\implies$ y3 = 7

$\large\underline\mathrm{Then,}$

$\implies$ 2(5 - 7) + 8(7 - 1) + k(1 - 5) = 0

$\implies$ 2(-2) + 8(6) + k(-4) = 0

$\implies$ -4 + 48 - 4k = o

$\implies$ 44 - 4k = 0

$\implies$ 4k = 44

$\implies$ k = 44/4

$\implies$ k = 11

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{The \: value \: of \: k \: is \: 11.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$