math stuff help....pls?

Question

okay here it goes...

one endpoint of a segment is (12,-8). the midpoint is (3,18). find the coordinates of the other endpoint.

a classmate tells you "findin the coordinates of a midpoint is easy. you just find the averages" is there any truth to it? explain what you think your classmate means.

find the 2 points on segment AB that divide the segment into three congruent parts. point A has coordinates (0,0) and point B has coordinates (9,6). explain your method.


thank you so much for your time and everything else

Answer 1

one endpoint of a segment is (12,-8). the midpoint is (3,18). find the coordinates of the other endpoint.
( (12+x)/2 , ( -8 + y)/2 ) = (3, 18)
so 12+x = 6 and -8 + y = 36
x = -6 and y = 44,
i.e. the coordinates of your point are: (-6, 44)

Answer 2

Let's do your second part first. He is correct, because the midpoint of (a,b) and (c,d) is ((a + c)/2,(b + d)/2).

Now let's get back to the first part. With one endpoint at
(12,-8) and the midpoint at (3,18), we are looking for a point (c,d) such that
((12 + c)/2,(-8 + d)/2) = (3,18). Equating coordinates we find (12 + c)/2 = 3, so c = -6. Similarly, we find d = 44.

Here is the idea for your third part. To divide a segment from (a,b) to (c,d) into three equal parts, we want

(1) from (a,b), to go 1/3 of the way from (a,b) to (c,d).

Similarly, for the other point, we want

(2) from (a,b), to go 2/3 of the way from (a,b) to (c,d).

From (1) we have our first point is (a,b) + (1/3)(c-a,d-b) =
(a + (1/3)*(c - a),b + (1/3)*(d - b) =
((2/3)a + (1/3)c,(2/3)b + (1/3)d). For the second point, we use (2) and find
((1/3)a + (2/3)c,(1/3)b + (2/3)d).

Anticipate this test question: How do you divide the segment from (a,b) to (c,d) into four equal parts?

Good luck.