Given:
The point
divides the line segment joining points
and
.
To find:
The ratio in which he point P divides the segment AB.
Solution:
Section formula: If a point divides a segment in m:n, then the coordinates of that point are,
![Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)](https://tex.z-dn.net/?f=Point%3D%5Cleft%28%5Cdfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%5Cdfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5Cright%29)
Let point P divides the segment AB in m:n. Then by using the section formula, we get
![\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%2C%5Cdfrac%7B5%7D%7B12%7D%5Cright%29%3D%5Cleft%28%5Cdfrac%7Bm%282%29%2Bn%28%5Cdfrac%7B1%7D%7B2%7D%29%7D%7Bm%2Bn%7D%2C%5Cdfrac%7Bm%28-5%29%2Bn%28%5Cdfrac%7B3%7D%7B2%7D%29%7D%7Bm%2Bn%7D%5Cright%29)
![\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%2C%5Cdfrac%7B5%7D%7B12%7D%5Cright%29%3D%5Cleft%28%5Cdfrac%7B2m%2B%5Cdfrac%7Bn%7D%7B2%7D%7D%7Bm%2Bn%7D%2C%5Cdfrac%7B-5m%2B%5Cdfrac%7B3n%7D%7B2%7D%7D%7Bm%2Bn%7D%5Cright%29)
On comparing both sides, we get
![\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B4%7D%3D%5Cdfrac%7B2m%2B%5Cdfrac%7Bn%7D%7B2%7D%7D%7Bm%2Bn%7D)
![\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B4%7D%28m%2Bn%29%3D%5Cdfrac%7B4m%2Bn%7D%7B2%7D)
Multiply both sides by 4.
![3(m+n)=2(4m+n)](https://tex.z-dn.net/?f=3%28m%2Bn%29%3D2%284m%2Bn%29)
![3m+3n=8m+2n](https://tex.z-dn.net/?f=3m%2B3n%3D8m%2B2n)
![3n-2n=8m-3m](https://tex.z-dn.net/?f=3n-2n%3D8m-3m)
![n=5m](https://tex.z-dn.net/?f=n%3D5m)
It can be written as
![\dfrac{1}{5}=\dfrac{m}{n}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B5%7D%3D%5Cdfrac%7Bm%7D%7Bn%7D)
![1:5=m:n](https://tex.z-dn.net/?f=1%3A5%3Dm%3An)
Therefore, the point P divides the line segment AB in 1:5.
Answer:
Step-by-step explanation:
<u><em>Q 4.</em></u> (25m + 25m) ÷ 25 sec. = <em>2 m/sec.</em>
<u><em>Q 5.</em></u> This question belongs to Physics and not Mathematics!!!
Wavelength (lambda) = Velocity (v) ÷ Frequency (
or Hz )
f = v / (lambda)
f = 3 / 2 = <em>1.5 (Hz)</em>
<u><em>Q 6.</em></u> 0.060 ÷ 2 = <em>0.030 m</em>
Step-by-step explanation:
X= raspberry
X = 600 ÷ 11 = 54 batches
[ 60 minutes = 1 hour]
[600 minutes = 10 hours]
Y = peach
Y = 600 ÷ 8 = 75 batches
Answer:A
Step-by-step explanation: im not too sure but i think 1-2/5=3/5 which would be red so
Answer:
Connect every other intersection of an arc and the circle with a segment.
Step-by-step explanation:
Connect every other intersection of an arc and the circle with a segment.