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2 years ago

If the figure is rotated 270° counterclockwise about the origin, what is the length of segment N′P′?

Mathematics

1 answer:

kap26 [50]2 years ago

7 0

Answer:

Option (2)

Step-by-step explanation:

Since, rotation of any figure is a rigid transformation, side lengths and measure of angles of the image polygon after rotation will remain same.

NP = N'P'

Coordinates of N → (5, 9)

Coordinates of P → (7, 9)

Formula of distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is,

d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

By this formula length of NP = $\sqrt{(7-5)^2+(9-9)^2}$

= 2 units

Therefore, Option (2) will be the correct option.

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

sergiy2304 [10]

Answer:

The measure of angle θ is 7π/6. The measure of its reference angle is 210°

and sin θ is -1/2.

Step-by-step explanation:

The correct question is:

The measure of angle θ is 7π/6. The measure of its reference angle is ___

and sin θ is ___

180° is equivalent to π radians. To transform 7π/6 radians to degrees, we have to use the following proportion:

180° / π radians = x° / (7π/6 radians)

x = (180/π) * (7π/6 radians)

x = 210°

And sin(210°) = -1/2

6 0

3 years ago

Complete the following proof. Prove: In an isosceles triangle, two medians are equal.

Paraphin [41]

Answer:

Midpoint of AB = (0 + 2a / 2 , 0 + 0 / 2) = (2a / 2 , 0 / 2) = (a,0)

x coordinate of point c = a

N = (0 + a / 2 , 0 + b / 2) = (a / 2 , b / 2)

M = ( 2a + a / 2 , 0 + b / 2) = (3a / 2 , b / 2)

MA = √(3a / 2 - 0)² + b / 2 - 0)²

= √(3a / 2 )² + (b / 2) = 9a² / 4 + b² / 4

NB = √(a / 2 - 2a)² + (b / 2 - 0 )²

= √( a / 2 - 4a / 2)² + (b / 2 - 0)²

= √(-3a / 2)² + (b / 2)² = √9a² / 4 + b² / 4

Step-by-step explanation:

I tried my best hope its correct :0

8 0

2 years ago

What is the exact value that is 48% of 1165

Vera_Pavlovna [14]

We know that the percentage amount of any number can be found by first converting the the given percentage to a fraction and then multiplying it by the given number. Thus, in our case, the exact value, that is 48% of 1165 can be calculated as follows:

We know that $48\%=\frac{48}{100}=0.48$