12. To rotate CW 270 degrees, find the points of the original triangle, make the Original X value becomes the new Y value and the new X value is the inverse of the original Y value.
B) to be in the same location as the original, it would be a 360 degree rotation.
13. to rotate 180 degrees mirror the image on the X and Y axis.
B) a 360 degree rotation.
See attached picture:
Answer:
Part A) The given enrollment numbers as a pair of points are (0,900) and (3,1,500)
Part B) The slope of the line is (see the explanation)
Part C)
Part D)
Step-by-step explanation:
Part A) Write the given enrollment numbers as a pair of points in the form (t,P)
Let
t ----> the number of years since 2009 (independent variable or input value)
P ---->the high school's student enrollment (dependent variable or output value)
we know that
For t=0 (year 2009) ----> P=900 students
so
The first ordered pair is (0,900)
For t=2012-2009=3 years ----> P=1,500 students
so
The second ordered pair is (3,1,500)
therefore
The given enrollment numbers as a pair of points are (0,900) and (3,1,500)
Part B) Find the slope of the line passing though the pair of points
we know that
The formula to calculate the slope between two points is equal to
we have
(0,900) and (3,1,500)
substitute the values
That means that the high school's student enrollment increase at rate of 200 students by year since 2009
Part C) Write an equation that relates the high school's student enrollment, P, to the number of years since 2009, t
we know that
The equation of a line in slope intercept form is equal to
where
m is the slope
b is the P-intercept
In this problem we have
---> represent the initial value ( value of P when the value of t is equal to zero)
substitute
Part D) Predict the high school's enrollment in 2017
For t=2017-2009=8 years
substitute the value of t in the linear equation
Answer:
P'(-3, -8), Q'(-6, 4), R'(1, -1)
Step-by-step explanation:
When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign: it becomes (x, -y).
Thus, if a point P, say, (-3, 8) is eightn units above the x-axis, its reflection P' will be the same distance below, at (-3, -8).
Thus, we get the following transformations.
P (-3, 8) ⟶ P' (-3, -8)
Q (-6, -4) ⟶ Q' (-6, 4)
R (1, 1) ⟶ R' (1, -1)
Thus, the vertices of the reflected triangle are P' (-3, -8), Q' (-6, 4), R' (1, -1).
The image below shows ∆PQR and its reflection ∆P'Q'R' across the x-axis.
