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satela [25.4K]
2 years ago
11

What is the image of the point (-5, 4) after a rotation of 270° counterclockwise

Mathematics
1 answer:
Illusion [34]2 years ago
5 0

Answer:

(4, 5)

Step-by-step explanation:

this is the same as a 90° rotation clockwise.

with the coordinates of (-5, 4) we start in the top left quadrant (x values are negative, y values are positive).

and we end up in the top right quadrant (x and y values are positive).

the line from the origin to the point is perpendicular (90° angle) to the line of the origin to the original point, as we just rotated by 90° or 270°.

that means the rules for the slope of perpendicular lines apply :

x and y coordinate differences trade places, and the sign of their ratio is flipped.

luckily, because the origin is the reference point for both lines, the point coordinates are automatically the coordinate differences to (0, 0).

and because we need to get 2 positive coordinates, that means

(-5, 4) turns into (4, 5)

as the alternative (-4, -5) would be in the bottom left quadrant.

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If 6 times a number = 3 times the same number,<br> that number must be this.
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The number must be 0, because any other number would multiply to a different product.
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3 years ago
Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius.
Eddi Din [679]

Step-by-step explanation:

volume = pi x radius² x height

okay so the cylinders diameter is 8 inches

diameter divided by 2 is radius so 8/2 = 4

so 3 times the radius will be 3x4 = 12

use the formula above and then you will get your answer

6 0
3 years ago
If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?
kondaur [170]

Equation of the circle is (x+6)^{2}+(y+10)^{2}=20.

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

Here, x_1=-8, y_1=-6, x_2=-4, y_2=-14

$P(x, y) =\left(\frac{-8-4}{2}, \frac{-6-14}{2}\right)

$P(x, y) =\left(\frac{-12}{2}, \frac{-20}{2}\right)

$P(x, y) =(-6, -10)

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}

Here, x_1=-6, y_1=-10, x_2=-8, y_2=-6

r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}

r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}

r=\sqrt{(-2)^{2}+(4)^{2}}

r=\sqrt{20} units

The standard form of the equation of a circle is

(x-a)^{2}+(y-b)^{2}=r^{2}, where (a, b) are center and r is the radius.

Here, center = (–6, –10) and r=\sqrt{20}

(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}

(x+6)^{2}+(y+10)^{2}=20

Equation of the circle is (x+6)^{2}+(y+10)^{2}=20.

4 0
3 years ago
Convert 203 yards into meters.
yuradex [85]

Answer:

184.73

Step-by-step explanation:

1 yard = 0.91m

203 yard=?

(203x0.91)/1=184.73.

+1(415) 450-6164

3 0
2 years ago
Can you help me solve this <br><br>Show your workings<br>​
True [87]
Card P is the answer
8*3=24
8*4=32
8*5=40
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2 years ago
Read 2 more answers
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