Let 'a' be the point and 'A' be the reflection of point 'a' through line x= -3
we know, (a+A)/2 (mid point of line aA) should lie on line x= -3
so by using this, we calculate vertices of reflected shape of MAST, we get
(-3,-1), (-3,2),(-5,3) and (-7,1)
Answer:
72 sides
Step-by-step explanation:
The sum of the angles of a polygon with n sides is (n−2) × 180
Since the polygon is regular, we can divide by the number of sides to find the measure of each angle (n−2) × 180 / n
Each angle is equal to 175
(n−2) × 180 / n = 175
Multiply each side by n
(n-2)180 = 175n
Distribute
180n -360 = 175n
Subtract 180n from each side
180n-180n-360 = 175n-180n
-360 = -5n
Divide each side by -5
-360/-5 =-5n/-5
72 = n
There are 72 sides
∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.
Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².
∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find
where 
is the length of the altitude originating from vertex O, and so
where 
is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².
So, the total area of the shaded region is
(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²
I think the boxes must be filled with
1/3 and -1/5.
