Answer:
The equation of the line is 7 x +5 y = 15.
Step-by-step explanation:
Here the given points are ( 5, -4) & ( -10, 17) -
Equation of a line whose points are given such that
( 
) & ( 
)-
y - 
= 
( x - 
)
i.e. <em>y - (-4)= 
( x- 5)</em>
<em> y + 4 = 
( x - 5)</em>
<em> y + 4 = 
( x - 5 )</em>
<em> ( y + 4) = 
( x - 5)</em>
<em> 5 (y + 4 ) = - 7 (x - 5 )</em>
<em> 5 y + 20 = -7 x + 35</em>
<em> 7 x + 5 y = 15</em>
Hence the equation of the required line whose passes trough the points ( 5, -4) & ( -10, 17) is 7 x + 5 y = 15.
Answer:
Step-by-step explanation:
ohhh this is easyyy its
Answer:
<h2>A's wrong.................(I Think)</h2>
Step-by-step explanation:
i think its D is B and D the same?
Answer:
![T = \left[\begin{array}{ccc}-\frac{1}{\sqrt{2} } &\frac{1}{\sqrt{2} }\\\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\end{array}\right]](https://tex.z-dn.net/?f=T%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%20%26%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%26%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Let General Transformation matrix be denoted as T
Step 1: Clockwise rotation of 45 degrees
General counterclockwise rotation matrix in 2-dimension is given as
![R(\theta)=\left[\begin{array}{ccc}cos\theta & - sin\theta\\sin\theta&cos\theta\\\end{array}\right]](https://tex.z-dn.net/?f=R%28%5Ctheta%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dcos%5Ctheta%20%26%20-%20sin%5Ctheta%5C%5Csin%5Ctheta%26cos%5Ctheta%5C%5C%5Cend%7Barray%7D%5Cright%5D)
For clockwise rotation we need to insert θ as negative in the above matrix. Therefore, the resulting matrix is
![R(-\theta)=\left[\begin{array}{ccc}cos\theta & sin\theta\\-sin\theta&cos\theta\\\end{array}\right]](https://tex.z-dn.net/?f=R%28-%5Ctheta%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dcos%5Ctheta%20%26%20sin%5Ctheta%5C%5C-sin%5Ctheta%26cos%5Ctheta%5C%5C%5Cend%7Barray%7D%5Cright%5D)
as sin(-θ) = -sin (θ) and cos(-θ) = cos (θ)
For 45 degrees
and 
![R(-45)=\left[\begin{array}{ccc}\frac{1}{\sqrt{2} } & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]](https://tex.z-dn.net/?f=R%28-45%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%20%20%26%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C-%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%26%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step 2: Reflection through line y = x
This type of reflection maps (x,y)→(y,x)
Therefore the general matrix is
![R(x,y)=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]](https://tex.z-dn.net/?f=R%28x%2Cy%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D)
Step 3: General Transformation Matrix
T = R(x,y) R(-θ)
![T=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}\frac{1}{\sqrt{2} } & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]](https://tex.z-dn.net/?f=T%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%20%20%26%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C-%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%26%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D)
