The equivalent 90° CCW rotation maps (x, y) to (-y, x).
(4, -2) becomes (2, 4) after rotation.
Answer: Angle ABC = 60, angle CBD = 120 and angle GFH = 60
Step-by-step explanation: Line ABD is parallel to line EFG. Line line CFH is a straight line that cuts across both parallel lines. Therefore, angle FBD and angle HFG are corresponding angles. That means angle FBD equals 3x. Also 3x plus 6X equals 180. That is,
3x + 6x = 180 {Sum of angles on a straight line equals 180}
9x = 180
Divide both sides of the equation by 9
x = 20.
That means angle 6x measures 6(20) and that is 120 degrees.
Also angle 3x measures 3(20) and that is 60 degrees.
Angle ABC + Angle CBD = 180 {Sum of angles on a straight line equals 180}
Angle ABC + 120 = 180
Angle ABC = 180 - 120
Angle ABC = 60
Also angle CBD equals 6x, and x = 20. Therefore angle CBD = 6 x 20
Angle CBD = 120.
And then, angle GFH = 3x, and x equals 20. Hence angle GFH = 60.
Therefore angle ABC = 60, angle CBD = 120 and angle GFH = 60.
Given
We have to set the restraint
because a square root is non-negative, and thus it can't equal a negative number. With this in mind, we can square both sides:
The solutions to this equation are 7 and -2. Recalling that we can only accept solutions greater than or equal to -1, 7 is a feasible solution, while -2 is extraneous.
Similarly, we have
So, we have to impose
Squaring both sides, we have
The solutions to this equation are 5 and 10. Since we only accept solutions greater than or equal to 7, 10 is a feasible solution, while 5 is extraneous.
357 is your answer because all you do is solve the problem =
Answer:
(- 1, - 6 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 270°
a point (x, y ) → (y, - x ), thus
(6, - 1 ) → (- 1, - 6 )
