What is the location of the image of P(−8, 1) after a counterclockwise rotation of 90° about (−2, 6) ?
1 answer:
Answer:
(3, 0)
Step-by-step explanation:
Given:
- Image: P = (-8, 1)
- Center of rotation: (-2, 6)
<u>Rotation rule</u> for -90°: (x, y) → (y, -x)
As the <u>center of rotation</u> is not the <u>origin</u>, we cannot simply apply the above rule.
To <u>rotate</u> an image around a <u>point other than the origin</u>:
1. Subtract each point of the image from the point of rotation:
⇒ Point of rotation - point of image
⇒ (-2, 6) - P = (-2, 6) - (-8, 1)
= (6, 5)
2. Rotate this about the origin by applying the rotation rule:
⇒ (x, y) → (y, -x)
⇒ (6, 5) → (5, -6)
Add the point of rotation to each rotated point of the image:
⇒ (5, -6) + (-2, 6) = (3, 0)
Therefore, the location of the image of P (-8, 1) after a counterclockwise rotation of 90° about (-2, 6) is (3, 0).
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Answer:
The monthly cost for 9 HCF is $38.54
Step-by-step explanation:
<em>The graph is missing; however, the question can still be solved</em>
Given
Slope = 1.55
When monthly cost = $47.84, Amount of water = 15 HCF
Required
Determine the monthly cost for 9 HCF
From the question, we understand that it is a linear function;
Linear functions are of the form
Where y is the function of x and m is the slope
In this case; the function is the monthly water bill
and x is the amount of water
Solving for b
When monthly cost = $47.84, Amount of water = 15 HCF
The function is as follows;
Subtract 23.25 from both sides
Solving for the monthly cost for 9 HCF
Here, we have that
Substitute these values in the linear function;
<em>Hence, the monthly cost for 9 HCF is $38.54</em>