Geometry midsegment

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rachelmaddie

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I need help with this question. Would I first use the midpoint formula for AB and AC to find the coordinates of P and Q? Then use the distance formula to find the length of PQ? 78955A27-AF29-4BCD-9EC5-BA6DCA571D1E.png
 
There are many ways to do this. Your approach should work. I see an easier solution, it involves similar triangles.
 
A(8,6)
B(1,1)
C(10,-3)

Using the midpoint formula
(x1+ x2/2) , (y1 + y2/2)

AB = (8+1/2), (6+1/2) = (4.5, 3.5)
AC = (8+10/2) , (6+(-3)/2) = (9, 1.5)

Find the difference between x and y coordinates.
(9 -4.5) = 4.5
(3.5 - 2.5) = 2
4.5 is the base, 2 is the height
To find the length of PQ use the Pythagorean theorem.
2^2 + 4.5^2 = c^2
4 + 20.25 = 24.25
Sqrt(24.25) = 4.92
Length of PQ = 4.92
Length of BC is 4.92 x 2 = 9.84
 
rachelmaddie said:
A(8,6)
B(1,1)
C(10,-3)

Using the midpoint formula
(x1+ x2/2) , (y1 + y2/2)

AB = (8+1/2), (6+1/2) = (4.5, 3.5)
AC = (8+10/2) , (6+(-3)/2) = (9, 1.5)

Find the difference between x and y coordinates.
(9 -4.5) = 4.5
(3.5 - 2.5) = 2
4.5 is the base, 2 is the height
To find the length of PQ use the Pythagorean theorem.
2^2 + 4.5^2 = c^2
4 + 20.25 = 24.25
Sqrt(24.25) = 4.92
Length of PQ = 4.92
Length of BC is 4.92 x 2 = 9.84
Click to expand...
You really need parentheses in the midpoint calculations.
I'm confused why you calculated length of BC as the last step. Considering you know the relationship between PQ and BC do you see a better solution?
 
lev888 said:
You really need parentheses in the midpoint calculations.
I'm confused why you calculated length of BC as the last step. Considering you know the relationship between PQ and BC do you see a better solution?
Click to expand...
Is that not correct the method?
 
rachelmaddie said:
I need help with this question. Would I first use the midpoint formula for AB and AC to find the coordinates of P and Q? Then use the distance formula to find the length of PQ? View attachment 14313
Click to expand...
Of course if you find the coordinates of P and Q and want the length PQ, then you use the distance formula. Think about this---what does the distance formula tell you and what information do you need to use the distance formula.
 
rachelmaddie said:
I need help with this question. Would I first use the midpoint formula for AB and AC to find the coordinates of P and Q? Then use the distance formula to find the length of PQ? View attachment 14313
Click to expand...
To rachelmaddie, if you only knew basic geometry, you would know that the line-segment joining the midpoints of two sides of a triangle is parallel to the the third side and is one-half the length of that third side. Had you know that then \(\displaystyle \|\overline{PQ}\|=\|\tfrac{1}{2}\|\overline{BC}\|\)
You can the length \(\displaystyle \|\overline{BC}\|\) so you are done.
 
pka said:
To rachelmaddie, if you only knew basic geometry, you would know that the line-segment joining the midpoints of two sides of a triangle is parallel to the the third side and is one-half the length of that third side. Had you know that then \(\displaystyle \|\overline{PQ}\|=\|\tfrac{1}{2}\|\overline{BC}\|\)
You can the length \(\displaystyle \|\overline{BC}\|\) so you are done.
Click to expand...
Yes, I know that PQ is one half of BC.
 
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