1. First transformation is rotation rotation of 180 about the origin. This transformation has a rule:
(x,y)→(-x,-y).
If points E(-2,-4), F(-1,-1), D(-2,-1) are vertices of triangle EFD, then
- E(-2,-4)→E''(2,4),
- F(-1,-1)→F''(1,1),
- D(-2,-1)→D''(2,1).
2. Second transformation is translation 1 unit left with a rule
(x,y)→(x-1,y).
Then
- E''(2,4)→E'(1,4),
- F''(1,1)→F'(0,1),
- D''(2,1)→D'(1,1).
Answer: 1st: rotation of 180 about the origin; 2nd: translation 1 unit left.
The equation in slope-intercept form represents a line that is parallel to y = 12x − 2 and passes through the point (−8,1) is y = 12x + 97
<em><u>Solution:</u></em>
Given that we have to write the equation in slope intercept form for line that is parallel to y = 12x − 2 and passes through the point (−8, 1)
<em><u>The slope intercept form is given as:</u></em>
y = mx + c ---- eqn 1
Where "m" is the slope of line and "c" is the y - intercept
Given equation of line is y = 12x - 2
On comparing the above equation with eqn 1,
m = 12
Thus slope of line is 12
We know that slopes of parallel lines are equal
Therefore, slope of line parallel to given line is also 12
Given point is (-8, 1)
We have to find the equation of line passing through (-8, 1) with slope m = 12
Substitute m = 12 and (x, y) = (-8, 1) in eqn 1
1 = 12(-8) + c
1 = -96 + c
c = 97
Substitute c = 97 and m = 12 in eqn 1
y = 12x + 97
Thus the required equation of line is found
Method 1: In order to find out the area of an octagon with a radius of 4 feet, we have to split the whole figure into 8 equal isosceles triangles.
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.
Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:
Area = 2√2 × r²
where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>
Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25
Rounded to the nearest tenth:
Area = 45.3 ft²
An imaginary number " i " is the squared root of -1, so whenever you square i it's like squaring a squared root. The squared root would cancel and you would be left with just the number under it, that is, the -1.
i ^ 2 = -1