anonymous
  • anonymous
A line segment has endpoints A(4, 8) and B(2, 10). The point M is the midpoint of AB. What is an equation of a line perpendicular to AB and passing through M?
Mathematics
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anonymous
  • anonymous
A line segment has endpoints A(4, 8) and B(2, 10). The point M is the midpoint of AB. What is an equation of a line perpendicular to AB and passing through M?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
ok you need to find the slope of the line
anonymous
  • anonymous
okay
anonymous
  • anonymous
use this formula \[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} } = m\]

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anonymous
  • anonymous
ok
anonymous
  • anonymous
I got y=-x+4
anonymous
  • anonymous
ok m is -1
anonymous
  • anonymous
okay
anonymous
  • anonymous
instead of 4 would it be
anonymous
  • anonymous
y=-x+c
anonymous
  • anonymous
plug in 1 of the point to the equation like this 8 = -1(4) +c Solve for c
anonymous
  • anonymous
i got 3
anonymous
  • anonymous
i got -4
anonymous
  • anonymous
umm c should be 12 8 = -4 +12
anonymous
  • anonymous
okay
anonymous
  • anonymous
now we find the midpoint of this line with this formula \[(\frac{ x _{1}+x _{2} }{ 2 } , \frac{ y _{1}+y _{2} }{ 2 })\]
anonymous
  • anonymous
okay
anonymous
  • anonymous
your midpoint should be (3,9)
anonymous
  • anonymous
okay
anonymous
  • anonymous
a. y = x + 4 b. y = −x + 4 c. y = −x + 6 d. y = x + 6 this is what I have to chose from
anonymous
  • anonymous
gradient of perpendicular line is \[m _{1}m _{1} = -1\] Since m1 is -1, we can assume m2 is 1
anonymous
  • anonymous
okay
anonymous
  • anonymous
so now we have y=x+c
anonymous
  • anonymous
we plug in the points of the midpoint into the equation we get 9 = 3 + c
anonymous
  • anonymous
it should be easy from here
anonymous
  • anonymous
12
anonymous
  • anonymous
umm no...look at it this way...3+ what number gives you 9?
anonymous
  • anonymous
6
anonymous
  • anonymous
yep so there you have it y=x+6
anonymous
  • anonymous
N is the midpoint of segment MP. O is the midpoint of segment NP. Segment MP with midpoint N and O M is located at (7, 8), and P is located at (14, -3). What are the coordinates of O? Select one: a. (-8.75, 4.25) b. (24.50, -0.50) c. (5.25, 1.25) d. (12.25, -0.25)
anonymous
  • anonymous
ok looks confusing but this is what they want|dw:1438267893606:dw|
anonymous
  • anonymous
Find the midpoint of MP with the formula i gave you earlier
anonymous
  • anonymous
okay
anonymous
  • anonymous
would it b C?
anonymous
  • anonymous
I meant to say would it be C
anonymous
  • anonymous
It's D
anonymous
  • anonymous
you want the solution?
anonymous
  • anonymous
yes
anonymous
  • anonymous
OK midpoint of MP is \[(\frac{ 7+14 }{ 2 },\frac{ 8+(-3) }{ 2 }) = (10.5, 2.5)\]
anonymous
  • anonymous
okay
anonymous
  • anonymous
N = (10.5,2.5), O is the midpoint of NP so \[(\frac{ 10.5+14 }{ 2 }, \frac{ 2.5+(-3) }{ 2 }) = (12.25,-0.25)\]
anonymous
  • anonymous
okay
anonymous
  • anonymous
A triangle has vertices at (4, 5), (4, -4), and (-4, -3). What is the approximate perimeter of the triangle? Select one: a. 27 b. 29 c. 28 d. 30 I got c for this on I just wanted to make sure if it was right or wrong
anonymous
  • anonymous
ok you need to find distance between the points with this formula \[\sqrt{(x _{2}-x _{1})+(y _{2}-y _{1})}\]
anonymous
  • anonymous
okay
anonymous
  • anonymous
so would I input which ever number to find the answer
anonymous
  • anonymous
no you need to get 2 points and put it into the formula to get the distance of 1 side of the triangle
anonymous
  • anonymous
okay
anonymous
  • anonymous
would be easier if you label it like A = (4,5) B = (4,-4) C =(-4,-3)
anonymous
  • anonymous
yes
anonymous
  • anonymous
Find the distance of AB and AC and BC then add them up
anonymous
  • anonymous
25?
anonymous
  • anonymous
lemme try
anonymous
  • anonymous
okay
anonymous
  • anonymous
I got 27
anonymous
  • anonymous
its C
anonymous
  • anonymous
okay
anonymous
  • anonymous
ill give you the distance you try and work it out AB = 9 AC = 11.31 BC = 8.06
anonymous
  • anonymous
I got 28 as well :D
anonymous
  • anonymous
i mean use the formula and try to see if you get the same distance
anonymous
  • anonymous
okay
anonymous
  • anonymous
yes
anonymous
  • anonymous
The volume of a sphere is 63089.813626667 cubic inches. What is the approximate diameter of this sphere? (Volume of a sphere = \frac{4}{3}\pi {r^3}) Select one: a. 5023.1 in b. 203.4 in c. 49.4 in d. 24.7 in I got b for this and I worked it out but I'm still not sure
anonymous
  • anonymous
\[63089.813626667 = \frac{ 4 }{ 3 } \pi r^3\] \[63089.813626667(\frac{ 3 }{ 4 }) = \pi r^3\] \[47317.36022 = \pi r^3\]
anonymous
  • anonymous
okay
anonymous
  • anonymous
\[\frac{ 47317.36022 }{ \pi } = 15061.58355 = r^3\] \[\sqrt[3]{15061.58355} = 24.69582535 = r\] \[dia. = 2r =24.69582535\times2 =49.39165069\]
anonymous
  • anonymous
so it's C
anonymous
  • anonymous
dayum sneaky teacher putting radius as an option

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