What will be the new position of the given point (6, -5) after rotating 90 degrees counterclockwise about the origin
Answers
Answer:
the new position of the point will be ()
Step-by-step explanation:
Please see the image for visualisation.
when we rotate any point A(x,y) counterclockwise about origin by some angle , then the coordinates of the new point B will change but the distance of A from origin would be the same as the distance from B.
i.e. |OA| = |OB| = =
.
Thus, by using trigonometry we can write the coordinates of B as
( ,
) where
is the angle that OB makes with positive x-axis.
Since OAB is a right angle triangle , AB=.
now , use distance formula to find the distance between A & B where use the coordinates of B as ( ,
) and A as (6,-5).
Equate this equation to .
Simplify and you will get that 12cos
= 10
sin
.
thus, Tan=
. now, use the image and you will see that sin
=6 and cos
=5.
Put these values in ( ,
) to get coordinates of B.
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