Question

Pls helpwill give the brainliest!Urgent!!need explanation.​

Answer 1

a)

The rotation transformations are:

$x=x' \cos \theta - y' \sin \theta\\y= x' \sin \theta + y' \cos \theta$

where $(x', y')$ are new coordinates.

Since we want an anti-clockwise rotation of the axes, put $\theta= 90$° to get the required coordinates as $(4,-1)$

b)

The equation of the given line is $x-y=0$

Use the mirror formula:

$x'= x_o - \frac{2 a}{a^2+ b^2}(a x_o + by_o +c)$

Replace $x$ by $y$ above to get the corresponding formula for the y-coordinate.

Here we have

$a=1$

$b=-1$

$c=0$

$x_o= 1$

$y_o =4$

Substitute these values to get the required coordinates as $(4,1)$

c)

$(5,3)$ maps onto $(1,1)$

Let's keep it simple here: To get the new coordinates you subtract 4 from the x coordinate and 2 from the y coordinate.

Thus for our point $(1,4)$ our image is $(1-4, 4-2)$ which is $(-3,2)$