PLS HELP pq has endpoints at p(-5,4) and q(7,-5).what is the midpoint of pq? what are the cordinates of the point 2/3 of the way from p to q? what is the length of pq?

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)