The area of the pentagon is 19 square units
The coordinates of the pentagon are given as:
The area of the pentagon is then calculated using:
So, we have:
Simplify the expressions in both brackets
Remove absolute bracket
Hence, the area of the pentagon is 19 square units
Read more about areas at:
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The distance traveled by the particle is given by the definite integral
where
is the path of the particle. The distance is then
The slope-intercept form is:
y = mx + b
where m = slope, and b = y-intercept.
You need a slope of 1, so m = 1.
You need a y-intercept of -1, so b = -1.
Replace m with 1 and b with -1 in the slope intercept form to get
y = 1x + (-1)
which simplifies to
y = x - 1
Standard form: Ax+By=C
first put in slope-intercept form:
slope = (0+5)/(6-3) = 5/3
pick point D: 0 = 5/3(6)+b -> b= -10
slope-intercept form: y=(5/3)x-10
multiply both sides by 3:
3y=5x-30
put in standard form:
5x-3y=30
