2) Find the point, M, that is five-sixths of the distance from A(-7, 2) to B(-1, -4).
1 answer:
We have that
point A(-7,2) and point B(-1,-4)
Step 1
find the distance AB
d=√[(-4-2)²+(-1+7)²]------------> √[36+36]
d=√72
step 2
find the point M
five-sixths of the distance from AB----------> (5/6)*√72
see the attached figure
AC/AB=x/((5/6)*AB)
6/(AB)=x/((5/6)*AB)--------> 6=6x/5
x=30/6-------> x=5
CB/AB=y/((5/6)*AB)
6/AB=y/((5/6)*AB)---------> 6=6y/5
y=30/6-------> y=5
therefore
the coordinate x of point M is
A(-7,2)
Mx=-7+5=-2
the coordinate y of point M is
A(-7,2)
My=2-5=-3
the point M is (-2,-3)
point A(-7,2) and point B(-1,-4)
Step 1
find the distance AB
d=√[(-4-2)²+(-1+7)²]------------> √[36+36]
d=√72
step 2
find the point M
five-sixths of the distance from AB----------> (5/6)*√72
see the attached figure
AC/AB=x/((5/6)*AB)
6/(AB)=x/((5/6)*AB)--------> 6=6x/5
x=30/6-------> x=5
CB/AB=y/((5/6)*AB)
6/AB=y/((5/6)*AB)---------> 6=6y/5
y=30/6-------> y=5
therefore
the coordinate x of point M is
A(-7,2)
Mx=-7+5=-2
the coordinate y of point M is
A(-7,2)
My=2-5=-3
the point M is (-2,-3)
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<u>Given</u>:
Given that the figure is a triangular prism.
The length of the prism is 4 m.
The base of the triangle is 2.5 m.
The height of the triangle is 2.25 m.
We need to determine the volume of the triangular prism.
<u>Volume of the triangular prism:</u>
The volume of the triangular prism can be determined using the formula,
where b is the base of the triangle,
h is the height of the triangle and
l is the length of the prism.
Substituting b = 2.5, h = 2.25 and l = 4 in the above formula, we get;
Thus, the volume of the triangular prism is 11.25 m³