## anonymous 5 years ago Consider the two points(1,-1) and(-3,-5) . The distance between them is: ? The x co-ordinate of the midpoint of the line segment that joins them is: ? The y co-ordinate of the midpoint of the line segment that joins them is?

1. anonymous

the distance between them is the length of the vector that comes from the difference between the coordinates. |dw:1327180152002:dw| the midpoint is the point that is the middle of that vector. |dw:1327180173361:dw| when you have that vector you devide its length by 2 to get half it's length. then depending on which direction your vector has (down left or up right) you place it on the (second point, first point) respectively and then the end of that vector has the coordinates of the midpoint of the line segment

2. anonymous

Ok thanks, so how can I tell which direction? Because it only gives me the coordinates...

3. anonymous

when you create any vector you can assume it starts at the origin 0,0 "you can paste them together and stuff but it sort of doesn't matter, it just an arrow with a particular length in a particular direction" like say call your vectors u and v, you can do u+v|dw:1327180790595:dw| or v+u|dw:1327180817392:dw| and that vector is the same sorta :P

4. anonymous

Oh ok, thanks, I just used the midpoint formula to solve it, and also the distance formula...

The first requirement was the distance of the line segment. Use the distance formula:$d=\sqrt{(1-(-3))^{2}+(-1-(-5))^{2}}$ $d=\sqrt{(\Delta x)^{2}+(\Delta y)^{2}}$$d \sqrt{4^{2}+4^{2}}=\sqrt{32}=4\sqrt{2}$

The second requirement is to find the x co-ordinate of the midpoint of the line segment that joins them is: ? This is the midpoint of distance of the c coordinate, the x values are +1 and -3. the midpoint is 1/2 the distance or -1 (-1, y)

The third requirement was:The y co-ordinate of the midpoint of the line segment that joins them is? Treat this similarly. The y distance is 4 take half (2) and locate the point down from the -1 or the point is -3. Midpoint is (-1,-3)