Question

Please answer the quickest and please don’t troll !!!

Answer 1

EXPLANATION

Let the required ratio be k : 1

by using section formula

X = mx2 + nx1 / m + n

Y = my2 + ny1 / m + n

c ( 7k + 2 / k + 1 ) , ( 8k + 3 / k + 1 )

Therefore

c = (4, 5) given

X =

x = 4 and y = 5

7k + 2 / k + 1 = 4

7k + 2 = 4k + 4

3k = 2

k = 2 : 3

Y =

8k + 3 / k + 1 = 5

8k + 3 = 5k + 5

3k = 2

k = 2/3

In each case k = 2/3

So the required ratio is 2/3 : 1

so ratio = 2 : 3 = ANSWER

Answer 2

☆GIVEN:

Point C(4,5) which is the division point of point A(2,3) and B(7,8)

☆TO FIND:

ratio in which the point C divides the join A and C.

☆SOLUTION:

Let the ration in which the point divides the join be k:1.

and;

$C(4;5)(x,y)$

$A(2,3)(x1,y1)$

$B(7,8)(x2,y2)$

☆By using the section formula;

$x = \frac{m \times x2 + n \times x1}{m + n}$

$y = \frac{m \times y2 + n \times y1}{m + n}$

here,

m and n is the ration in which the join divides.

Coming to main question;

Here;

m = k

n = 1

$4 = \frac{k \times 7 + 1 \times 2}{k + 1}$

$4 = \frac{7k + 2}{k + 1} \\ 4(k + 1) = 7k + 2 \\ 4k + 4 = 7k + 2 \\ 4 - 2 = 7k - 4k \\ 2 = 3k \\ \frac{2}{3} = k$

So,

k = 2/3

required ratio is;

$\frac{ \frac{2}{3} }{1}$

☆FINAL ANSWER IS :

$\frac{2}{3}$