Here, Let coordinates = ( 0, y)
Let, y-axis divides line in the ratio = k : 1
Now, (0, y) = [(10k-4) / k+1 , (12k-6)/ k + 1 ]
0 = 10k - 4 / k+1
10k = 4
k = 4/10 = 2/5
In short, Your ratio of division would be: 2 : 5
Now, y = (12k - 6)/ k + 1
y = 12*2/5 - 6 / 2/5 + 1
y = -6/7
In short, Your Coordinates would be: (0, -6/7 )
Hope this helps!
Answer:
B = (-7,10)
Step-by-step explanation:
Given that , a line AB has midpoint (-2,4) and the coordinates of A is ( 3 , -2). We need to find out the coordinates of B .
- Let coordinate of B be ( p,q ). We can use midpoint formula , as ,
=> Midpoint = ( x₁ + x₂ / 2 , y₁ + y₂/2 )
=> ( -2,4 ) = ( p + 3)/2 , ( q -2 )/2
=> -2 = p + 3/2
=> p + 3 = -4
=> p = -3 - 4
=> p = (-7)
<u>Also </u><u>:</u><u>-</u><u> </u>
=> q - 2/2 = 4
=> q -2 = 8
=> q = 8 + 2
=> q = 10
<h3>
<u>Hence</u><u> the</u><u> </u><u>coordinates</u><u> </u><u>of </u><u>B </u><u>is</u><u> </u><u>(</u><u> </u><u>-</u><u>7</u><u>,</u><u>1</u><u>0</u><u> </u><u>)</u><u> </u><u>.</u></h3>
The friend lives in a town that is 10° farther north than 40° N. The latitude of that town is 40° +10° = 50° N. When that latitude is reflected across the equator, N changes to S. The new latitude would be c. 50° S.
![\begin{cases}4x+3y=11\\-4x+6y=-2\end{cases}\\\\\\\\ \left[\begin{array}{cc}4&3\\-4&6\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}11\\-2\end{array}\right]\\\\\\\\A=\left[\begin{array}{cc}4&3\\-4&6\end{array}\right]\\\\\\\\A^{-1}=\dfrac{1}{4\cdot6-3\cdot(-4)}\left[\begin{array}{cc}6&-3\\4&4\end{array}\right]=\dfrac{1}{24+12}\left[\begin{array}{cc}6&-3\\4&4\end{array}\right]=](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D4x%2B3y%3D11%5C%5C-4x%2B6y%3D-2%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%5C%20%20%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%263%5C%5C-4%266%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C-2%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5C%5CA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%263%5C%5C-4%266%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5C%5CA%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7B4%5Ccdot6-3%5Ccdot%28-4%29%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-3%5C%5C4%264%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B24%2B12%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-3%5C%5C4%264%5Cend%7Barray%7D%5Cright%5D%3D)
![=\dfrac{1}{36}\left[\begin{array}{cc}6&-3\\4&4\end{array}\right]=\left[\begin{array}{cc}\frac{1}{6}&-\frac{1}{12}\\\\\frac{1}{9}&\frac{1}{9}\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B36%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-3%5C%5C4%264%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B1%7D%7B6%7D%26-%5Cfrac%7B1%7D%7B12%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7B9%7D%26%5Cfrac%7B1%7D%7B9%7D%5Cend%7Barray%7D%5Cright%5D)
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