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anzhelika [568]
3 years ago
9

What is (2,7) rotated 90% clockwise

Mathematics
1 answer:
ohaa [14]3 years ago
5 0

Answer:

The required point is, (7, -2)

Step-by-step explanation:

The straight  line passing through (0,0) and (2,7) is,

y = (\frac {7 -0}{2-0}) \times x

⇒ y = 3.5x --------------(1)

Now, the straight line perpendicular to this line and passing through (0, 0) is

y = (\frac {-1}{3.5}) \times x

⇒ 7y + 2x = 0 -------------(2)

Let, (h,k) be the required point.

then, it is on the line 7y + 2x = 0

⇒7k + 2h = 0

⇒k = (\frac {-2}{7}) \times h ------------(3)

Again, distance from (0,0) of (h, k) is same as that of (2,7)

⇒ h^{2} + k^{2} = 4 + 49 = 53

⇒h^{2} \times (\frac {53}{49}) = 53 [putting the value of k from (3)]

⇒h^{2} = 49

⇒h = 7 [since, (h,k) is in 4th quadrant, so,h >0]

So, k = -2 [putting the value of h in (3)]

So, the required point is, (7, -2)

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What is the area of the composite figure? (use 3.14 for pi). Explain how you arrived at your answer. Please round to the nearest
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The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

Step-by-step explanation:

The given is,

                 Given diagram is combination of Rectangle and Semi circle.

Step:1

         Res the attachment,

                      Area of given diagram = Area of A + Area of B..............(1)

Step:2

         For A,

         The A section in the given diagram is semi circle,

                     Diameter of semi circle = Total distance - ( 2+3)

                                          ( ∵ 2, 3 are top distance in the given diagram)

                                                             = 10 - 5

                                        Diameter, d = 5 cm

                                             Radius, r = \frac{d}{2}

                                                          r = \frac{5}{2}

                                                         r = 2.5 cm

                                          Area, A_{A}  = \frac {\pi r^{2} }{2}........................(2)

                                                    A_{A}  = \frac {\pi (2.5)^{2} }{2}  

                                                           = \frac {\pi ( 6.25) }{2}

                                                           = \frac{19.63}{2}

                                                     A_{A} = 9.8174 cm^{2}

Step:3

               For B,

               Area of rectangle is,

                                                      A_{B} =lb.....................(3)

              Where, l - Length = 10 cm

                          b - Width = 2 cm

              Equation (3) become,

                                                            = (10)(2)

                                                            = 20

                                    Area of B, A_{B} = 20 cm^{2}

Step:4

               From the equation (1),

                               Area of given diagram = 20+ 9.81747

                                                            Area = 29.817 square centimeters

Result:

            The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

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You know a fraction responds to a terminating decimal because it can be simplified to a terminating decimal.

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