Answer:
X''(2, -5), Y''(3, -3)
Step-by-step explanation:
You know that reflection in the x-axis changes the sign of the y-coordinate. Points that used to be above the axis are now below by the same amount, and vice versa.
Rotation counterclockwise by 270° is the same as clockwise rotation by 90°. That maps the coordinates like this:
(x, y) ⇒ (y, -x)
The two transformations together give you ...
(x, y) ⇒ (x, -y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection across y=-x.
Using this mapping, we have ...
X(5, -2) ⇒ X''(2, -5)
Y(3, -3) ⇒ Y''(3, -3) . . . . . . on the equivalent line of reflection, so invariant
_____
The attachment shows the original segment in red, the reflected segment in purple, and the rotated segment in blue. The equivalent line of reflection is shown as a dashed green line.
Answer:
84 sq meters
Step-by-step explanation:
1. Approach
In order to solve this problem, one will have to divide the figure up into simple shapes. A picture is attached showing how the shape is divided up for this answer. Find the area of each region, then add up the results to find the total area.
2. Area of Region 1
As one can see, the length of (Region 1), as given is (6), the width is (3). To find the area multiply the length by the width.
Length * width
6 * 3
= 18
3. Area of Region 2
In (Region 2), the length is given, (12). However, one must find the width, this would be the size of the total side, minus the width of (Region 1). Multiply the length by the side to find the area.
Length * width
= 12 * (8 - 3)
= 12 * 5
= 60
4. Area of Region 3
In (Region 3), the length of the figure is (2), the width is (3). To find the area, multiply the length by the width.
Length * width
= 2 * 3
= 6
5. Total area
Now add up the area of each region to find the total rea,
(Region 1) + (Region 2) + ( Region 3)
= 18 + 60 + 6
= 84
Answer:
h = A/πr²
Step-by-step explanation:
Surface area (A) of a cylinder = πr² × height (h) , where r is the radius.
h = A ÷ πr² = A/πr²
-8
f(-1/2)=10(-1/2)-3
f(-1/2)=(-5)-3
f(-1/2)=-8
