3 years ago

What is the image of point R after a counterclockwise rotation on 270 degrees about the orgin?

1 answer:

alexandr1967 [171]3 years ago

4 0

I will use ccw for countercloclwise and cw for clockwise for this explination.

A 270 ccw rotation is the EXACT same as a 90 cw rotation. So to perform a 90 degree cw rotation all that has to be done is swap the x anf y coordinates and change the sign on the y. As a general form:
(x, y) becomes (y, -x)

In your problem R is at (3, 6) so swap the 3 and 6 to get (6, 3) now change the sign on the 3 to get R' as (6, -3)

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3 years ago

Find all complex solutions of 5x^2-6x+2=0.

gregori [183]

We use quadratic formula for that one
remember that √-1=i

so

for
ax^2+bx+c=0
$x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$
so
given
5x^2-6x+2=0
a=5
b=-6
c=2

$x=\frac{-(-6)+/-\sqrt{(-6)^2-4(5)(2)}}{2(5)}$
$x=\frac{6+/-\sqrt{36-40}}{10}$
$x=\frac{6+/-\sqrt{-4}}{10}$
$x=\frac{6+/-2i}{10}$

$x=\frac{3}{5}+\frac{i}{5}, \frac{3}{5}-\frac{i}{5}$