Answer:
a. (1, -0.5)
b. (-0.2, 0.4)
c. 15 units
Step-by-step explanation:
a. The midpoint of PQ
To calculate this, we use the midpoint formula;
(x,y) = {(x1 + x2)/2 , (y1 + y2)/2}
From the question; (x1,y1) = (-5,4) and (x2,y2) = (7,-5)
So (x,y) = (-5+7)/2 , (4-5)/2 = 2/2, -1/2 = (1,-0.5)
The coordinates of the midpoint of pq is (1,-0.5)
c. Length of pq
Mathematically;
Length = √{(x2-x1)^2 + (y2-y1)^2}
Length = √{(7-(-5))^2 + (-5-4)^2}
Length = √(12)^2 + (-9)^2
Length = √(144 + 81) = √(225) = 15
b. What we will use here is the internal division formula of the section formula;
Mathematically the coordinates can be calculated using the formula;
(x,y) = (mx2 + nx1)/m+ n , (my2 + ny1)/m + n
in this case, m = 2 and n = 3
(x1,y1) = (-5,4)
(x2,y2) = (7,-5)
So substituting these values, we have;
(x,y) = (2(7)+ 3(-5))/(2+3) , 2(-5) + 3(4)/(2+3)
(x,y) = (14 -15)/5 , (-10 + 12)/5
= (-1/5, 2/5) = (-0.2, 0.4)
. If 
is in the third quadrant, then 
and 
. Recall that
to be negative, so we take the negative root. We end up with
