HELP PLEASE 10 POINTS
2 answers:
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Answer:
A) (5, 7π/4): (5, 15π/4) and (-5, 3π/4)
B) (−6, π/2): (−6, 5π/2) and (6, -π/2)
C) (5, −2): (5, 2π-2) and (-5, -π-2)
Step-by-step explanation:
To find pair of coordinates for (r>0), add 2π to corresponding θ. For (r<0) subtract π from given angle to find second pair of coordinate.
A) (5, 7π/4)
For (r>0)
θ = 7π/4 + 2π
θ = 15π/4
Point is (5, 15π/4)
For (r<0)
θ = 7π/4 - π
θ = 3π/4
Point is (-5, 3π/4)
As it can be seen in Fig 1
(5, 7π/4)=(5, 15π/4)=(-5, 3π/4)
B) (−6, π/2)
For (r>0)
θ = π/2 + 2π
θ = 5π/2
Point is (6, 5π/2)
For (r<0)
θ = π/2 - π
θ = -π/2
Point is (-6, -π/2)
As shown in fig 2
(-6, π/2) = (6, 5π/2) = (-6, -π/2)
C) (5, −2)
For (r>0)
θ = -2 + 2π
Point is (5, 2π-2)
For (r<0)
θ = -2 - π
Point is (-5, -π)
As shown in Fig. 3
(5, −2) = (5, 2π-2) = (-5, -π)
Answer:
The equation of the parallel line is x + 3y = 17
Step-by-step explanation:
Parallel lines have the same slopes and different y-intercept
The form of the equation y = m x + b, where
- m is the slope of the line
- b is the y-intercept
∵ The equation of the given line is x + 3y = 4
→ We must put it in the form above to find its slope
→ Subtract x from both sides to move x to the right side
∵ x - x + 3y = 4 - x
∴ 3y = 4 - x
→ Divide both sides by 3 to make the coefficient of y = 1
∴
∴ y = -
x
→ Compare it with the form of the equation above
∴ m =
∵ Parallel lines have the same slopes
∴ The slope of the parallel line is
→ Put it in the form of the equation
∴ y = x + b
→ To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ The line passes through the point (2, 5)
∴ x = 2 and y = 5
→ Substitute them in the equation
∴ 5 = (2) + b
∴ 5 = + b
→ Add to both sides
∴ = b
→ Substitute it in the form of the equation above
∴ y = x +
→ Multiply each term by 3
∴ 3y = - x + 17
→ Add x to both sides
∴ x + 3y = 17
∴ The equation of the parallel line is x + 3y = 17