Answer: 90 degrees clockwise
This is equivalent to 270 degrees counterclockwise
The rule for either rotation is
The x and y coordinates swap places, and the new second coordinate flips from positive to negative (or vice versa).
The diagram below shows an example of this for the point (-4,-2) rotating to (-2, 4). The center of the rotation is the origin (0,0).
Given:
In a right angle triangle θ is an acute angle and .
To find:
The value of .
Solution:
In a right angle triangle,
We have,
It means the ratio of perpendicular to base is 3:5. Let 3x be the perpendicular and 5x be the base.
By using Pythagoras theorem,
In a right angle triangle,
Therefore, the value of is
.
Answer is option C
Mr. Jones jogs the same route each day. The amount of time he jogs is inversely proportional to his jogging rate.
k is the constant of proportionality
We check with each option and identify which option gives us same K value
(a) 4 mph for 2.5 hours and 6 mph for 3.75 hours
so k = 10
so k = 22.5
K values are not same
(b) 3 mph for 2 hours and 4.5 mph for 3 hours
so k = 6
so k = 13.5
K values are not same
(c) 4 mph for 2.5 hours and 5 mph for 2 hours
so k = 10
so k =10
K values are same .
Answer is option C