Find the coordinates of the point which divides the join of (-1,7) and (4.-3) in the ratio 2:3 ??
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Answers
Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3 ?
Solution:-Let the given points be A(-1,7) and B(4,-3)
Now,
Let the point be P(x, y) which divides AB in the ratio 2:3
Here,
[tex] { \bf x \: = \frac{m_1 x_2 \: + \: m_1 x_1}{m_1 \: + \: m_2}} [/tex]Where,
[tex] m_1 [/tex] = 2 , [tex] m_2 [/tex] = 3
[tex] x_1 [/tex] = -1 , [tex] x_2 [/tex] = 4
[tex] \therefore [/tex] Putting values we get,
x = [tex] \frac{2 \: × \: 4 \: + \: 3 \: × \: -1}{2 \: + \: 3} [/tex]
x = [tex] \frac{8 \: - \: 3}{5} [/tex]
x = [tex] \frac{5}{5} [/tex]
x = 1
Now,
Finding y
[tex] { \bf y \: = \frac{m_1 y_2 \: + \: m_2 y_1}{m_1 \: + \: m_2}} [/tex]Where,
[tex] m_1 [/tex] = 2 , [tex] m_2 [/tex] = 3
[tex] x_1 [/tex] = 7 , [tex] x_2 [/tex] = -3
[tex] \therefore [/tex] Putting values we get,
y = [tex] \frac{2 \: × \: -3 \: + \: 3 \: × \: 7}{2 \: + \: 3} [/tex]
y = [tex] \frac{-6 \: + \: 21}{5} [/tex]
y = [tex] \frac{15}{5} [/tex]
y = 3
Hence x = 1, y = 3
So, the required point is P(x, y)
= P(1, 3)
The coordinates of the point is P(1, 3). [Answer]_______________________________________
Note:- Refer the attachment.
_______________________________________
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Calculation of VolumeStorage locker A is 6 feet wide, 6 feet deep, and has a height of 9 feet.
Volume of the cuboid is length times width times height
[tex]volume \; of \; locker \; A = lwh\\=6 \cdot 6 \cdot 9\\=324 cubic feet[/tex]
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Volume locker B is 306 cubic feet.
324 cubic feet is bigger thatn 306 cubic feet.
Locker A is bigger.
The monthly rent for Locker A is $0.35 per cubic foot. The monthly rent for Locker B is $0.40 per cubic foot.
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Monthly rent for 324 cubic feet is [tex]324 \cdot 0.35 =113.4[/tex]
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