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DerKrebs [107]
3 years ago
11

Determine the ratio in which the point (–6, m) divides the join of A(–3, –1) and B(–8, 9). Also, find the value of m.

Mathematics
2 answers:
ser-zykov [4K]3 years ago
5 0

Answer:

m=5

Step-by-step explanation:

Given: Point C(x_3,y_3)=(-6,m) divides the join of point A(x_1,y_1)=(-3,-1) and point B(x_2,y_2)=(8,9)

Let the line AB divides by Point C in a ratio m:n=k:1

Then, Using section formula   (x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}

Applying formula,

x_3,y_3=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}

x_3,y_3=\frac{-8k-3}{k+1},\frac{9k-1}{k+1}

But, x_3=-6

Therefore,  x_3=\frac{-8k-3}{k+1}

-6=\frac{-8k-3}{k+1}

-6k-6=-8k-3

2k-3=0

k=\frac{3}{2}

Therefore, C divides line AB in 3:2

Now,  m=\frac{9k-1}{k+1}  where, k=3/2

m=\frac{9\frac{3}{2}-1}{\frac{3}{2}+1}

m=\frac{\frac{25}{2}}{\frac{5}{2}}

m=\frac{25\times2}{2\times5}

m=5


PSYCHO15rus [73]3 years ago
4 0

Answer:

Ratio = 3 : 2 and value of m = 5.

Step-by-step explanation:

We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.

Let us assume that it cuts the line in k : 1 ratio.

Then, the co-ordinates of P = ( \frac{-8k-3}{k+1},\frac{9k-1}{k+1} ).

But, \frac{-8k-3}{k+1} = -6

i.e. -8k-3 = -6k-6

i.e. -2k = -3

i.e. k = \frac{3}{2}

So, the ratio is k : 1 i.e \frac{3}{2} : 1 i.e. 3 : 2.

Hence, the ratio in which P divides the line is 3 : 2.

Also, \frac{9k-1}{k+1} = m where k = \frac{3}{2}

i.e. m = \frac{\frac{9 \times 3}{2}-1}{\frac{3}{2}-1}

i.e. m = \frac{27-2}{3+2}

i.e. m = \frac{25}{5}

i.e. m = 5.

Hence, the value of m is 5.

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