Answer:
Explanation:
equation of finding a midpoint is (x2+x1)/2 and (y1+y2)/2
7) (4+12)/2 = 8 and (9+-4)/2= 2.5
hence midpoint is (8,2.5)
8) we are told the midpoint so we can now find the co-ordinates of the other endpoint:
(5+x)/2= -3
rearrange to find x--> 5+x =-6, so x=-11
(-7+y)/2=2
rearrange to find y--> -7+y=4, so y=11
other endpoint: (-11,11)
5) the gradient of the new equation is parallel to y=3x+7 so it will stay the same
y=3x+c
we know that the points this line passes through is: (-4,-8) so we substitute this into our new equation to find c
-8= (3 x -4) +c
-8=-12 +c
so c= 4
Hence our new equation is y=3x+4
6) perpendicular gradient means that our existing gradient needs to be reciprocated (turned into negative and then flipped)
new gradient is -1/3
y=-1/3x+c
we know the value for x and y so we can substitute into our new equation to find c
9=(-1/3 x -6) +c
9=2 + c
c= 7
Hence our new equation is y=-1/3x+7
Hope this helps!