Answer:
Step-by-step explanation:
Given
Required
Determine the value of k
First, we need to determine the equation of g(x)
Start by calculating the slope (m)
Where x and y are two corresponding values:
The slope (m) is:
The equation is calculated using:
Where
and
Make y the subject of formula
So:
Next, we determine the equation of f(x)
Start by calculating the slope (m)
Where x and y are two corresponding values:
The slope (m) is:
The equation is calculated using:
Where
and
Make y the subject of formula
So:
Recall that
Make k the subject
Substitute values for g(x) and f(x)
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ANSWER
EXPLANATIONSolve for x, noting that scalar multiplication on matrices is distributive:
Note that
and
Therefore, since we add corresponding entries with matrix addition:
<u>Solution-</u>
1- When rotating a figure 180 degrees around the origin (As it does not matter whether you move clockwise or counter-clockwise), we apply the rule (x, y) → (-x, -y).
Co-ordinates of the vertices,
P = (1, -1)
Q = (3, -2)
R = (3, -4)
And then calculating the co-ordinates of P', Q', R'
P' = (-1, 1)
Q' = (-3, 2)
R' = (-3, 4)
2- When reflecting a figure across X-axis, we apply the rule (x, y) → (x, -y).
Co-ordinates of the vertices,
P' = (-1, 1)
Q' = (-3, 2)
R' = (-3, 4)
And then calculating the co-ordinates of P'', Q'', R''
P'' = (-1, -1)
Q'' = (-3, -2)
R'' = (-3, -4)