Question

PLEASE HELP, I’ve been stuck on this question for a whileIn the diagram, AB is divided into equal parts. The coordinates of point A (-3,9), and the coordinates of point B are (9,5).
The coordinates of point C are _____
{Options:
(-1.5,10.5)
(-1.5,8.5)
(-0.5,8.5)
(-0.5,10.5)
The coordinates of point E are _____
{Options:
(1,5,6.5)
(1.5,7.5)
(2.5,6.5)
(2.5,7.5)
The coordinates of point H are _____
{Options:
(5,5.5)
(5,6)
(6,5)
6,6)

Answer 1

The coordinates of point C are (-1.5, 8.5)

The coordinates of point E are (1.5, 7.5)

The coordinates of point H are (6, 6)

This is for Plato

Answer 2

AB is divided into 8 equal parts and point C is 1 part FROM A TO B, so the ratio is 1:7, with C being 1/7 of the way.  The ratio is k, found by writing the numerator of the ratio (1) over the sum of the numerator and denominator (1+7).  So our k value is 1/8.  Now we need to find the rise and the run (slope) of the points A and B.  $m= \frac{5-9}{9-(-3)}$.  That gives us a rise of -4 and a run of 12.  The coordinates of C are found in this formula: $C(x,y)=[ x_{1} +k(run), y_{1} +k(rise)]$.  Filling in accordingly, we have $C(x,y)=[-3+ \frac{1}{8}(12),9+ \frac{1}{8}(-4)]$ which simplifies a bit to $C(x,y)=(-3+ \frac{3}{2},9- \frac{1}{2})$.  Finding common denominators and doing the math gives us that the coordinates of point C are $(- \frac{3}{2}, \frac{17}{2})$.  There you go!