Question

16. If the points (x, 9), (0, 1) and (-6, -7) are collinear, then the value of x is
(x, 9), 10, 1) మరియు 1-6, 7) బిందువులు సరేఖీయాలైతే x విలువ
(
14
(215
(316
SPACE FOR ROUGH WODY
147​

Answer 1

$Let \: A(x,9) = (x_{1},y_{1}) ,B(0,1)= (x_{2},y_{2}) ,$

$C(-6,-7) = (x_{3},y_{3}) \:are \: collinear \:points$

$Area \:of \: \triangle ABC = 0$

$\implies \frac{1}{2}| x_{1}(y_{2}-y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2})| = 0$

$\implies |x(1+7)+0(-7-9)+(-6)(9-1)| = 0$

$\implies | 8x-48| = 0$

$\implies 8x = 48$

$\implies x = \frac{48}{8}$

$\implies x = 6$

Therefore.,

$\red{ Value \: of \: x }\green { = 6 }$

•••♪

Answer 2

Answer:

3)6

Step-by-step explanation:

let

ABC

A=(x,9),B=(0,1),C=(–6,–7)

Now we have area of triangle

1/2(x1(y2–y3)+x2(y3–y1)+x3(y1–y2))

1/2(x(1‐(‐7))+0(-7–9)+–6(9-1))

1/2(x(-7)+0(‐16)–6(8)

1/2(x(-7)–16–48)

1/2(x-7)–64

1/2(x)(–448)

1/2