Question

I

15. Find the coordinates of D, the midpoint of AB.
16. Find the length of the median CD.
17. Find the coordinates of the centroid. Label this point as G.

Answer 1

Explanation:

15) point D=(3,1)

for AB we can see that there is an exact triangle of 2 and 5

so AD =
`\sqrt{2^(2) +5^(2) }` =
`√(29)` and 2(AD) = AB

AB = 2*
`√(29)` ( this is an exact answer, leave it with the square root)

16) find CD length we know the points at each end so use the distance formula P1=(-3,4) P2=(3,1)

Dist. =
`\sqrt{(3-(-3))^(2) +(1-4)^(2) }`

Dist. =
`√(45)` =
`√(9*5)` = 3
`√(5)` ( exact answer leave the square root )

CD = 3
`√(5)`

17) 1/3 of the way along CD from D towards C is where the centroid is.. I just happen to know that from doing this too often. :/

so that mean
`(1)/(3)` *
`3√(5)` is the distance from D to the centroid or
`√(5)`

also b/c I happen to know.. :/ c =
`\sqrt{1^(2)+ 2^(2) }` =
`√(5)` off the top of my head I can see that the point (1,2) is our centroid for this object.. they made it really easy ... okay.. relatively easy. .:D

Centroid = (1,2)