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1 year ago

Rotate the following figure 90° counterclockwise about the origin: l: (-3,-4), J: (-4, 0), K: (-3, O), L: (0, -2)

Mathematics

1 answer:

Juliette [100K]1 year ago

5 0

Let's begin by identifying key information given to us:

$I(-3,-4),J(-4,0),K(-3,0),L(0,-2)$

We are to rotate the figure 90 degrees counterclockwise about the origin. The transformation is mapped by the formula:

$\begin{gathered} A\mleft(x,y\mright)\rightarrow A^{\prime}\mleft(-y,x\mright) \\ I(-3,-4)\rightarrow I^{\prime}(4,-3) \\ J\mleft(-4,0\mright)\rightarrow J^{\prime}(0,-4) \\ K\mleft(-3,0\mright)\rightarrow K^{\prime}(0,-3) \\ L\mleft(0,-2\mright)\rightarrow L^{\prime}(2,0) \end{gathered}$

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The interior angle of a regular polygon is five times its corresponding exterior angle. Find the

tiny-mole [99]

Answer:

Step-by-step explanation:

Regular polygon is one in which each angle and sides is congruent.

Sum of all the exterior angles of any polygon is 360.

Sum of all the interior angles of any polygon is (2n-4)*90

where is n is the no. of sides of polygon.

Let n be the no. of sides of polygon required

Therefore,

Sum of all the interior angles of polygon = (2n-4)*90

since no of sides of polygon is n

therefore, value of each interior angles of the polygon = (2n-4)*90/n (A)

Sum of all the exterior angles of any polygon = 360.

value of each exterior angles of the polygon = 360/n (B)

Given that

The interior angle of a regular polygon is five times its corresponding exterior angle (c)

using the statement A, B and C

(2n-4)*90/n = 5*360/n

1/n is common on both side, hence it gets cancelled.

(2n-4)*90 = 5*360

=> (2n-4) = 5*360 /90 = 20

=> 2n = 20+4 = 24

=> n = 24/2 = 12.

the number of sides of the polygon is 12

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3 years ago

Can the ratio of a parent age to his or her childs age ever be exactly 3:2?

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Yes beacuse that means it would be 32 years old

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4 years ago

Read 2 more answers

line segment with one endpoint at (2,5) is divided in the ratio 4:5 by the point (10,1). which coordinates could represent the o

rodikova [14]

Answer:

(20,-4)

Step-by-step explanation:

We are given;

One end point as (2,5)

Point of division as (10,1)

The ratio of division as 4:5

We are required to calculate the other endpoint.

Assuming the other endpoint is (x,y)

Using the ratio theorem

If the unknown endpoint is the last point on the line segment;

Then;

$\left[\begin{array}{ccc}10\\1\end{array}\right]$ = $\frac{4}{5} \left[\begin{array}{ccc}x\\y\end{array}\right]$ + $\frac{5}{9}\left[\begin{array}{ccc}2\\5\end{array}\right]$