Question

point x (6,4) and y (-4,-16) are the endpoint of XY. what are the coordinates of point Z on XY such that XZ is 4/5 the length of XY
a) (4,0)
b) (0,-8)
c) (1,-6)
d) (-2,-12)

Answer 1

distance is
\[d=\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^2}\]
d= sqrt (-4-6)^2 + (-16-4)^2
d= sqrt (-10)^2 + (-20)^2
d= sqrt 100+400
d=sqrt 500
d=22.36

The distance from point x to point y is about 22.36.
4/5 of this distance is 17.888 (.8 * 22.26)

So the distance from X to Z has to be 17.888

17.888=sqrt (x2-6)^2 + (y2-4)^2
you can guestimate from here with the answer choices


looking at the graph, you know Z will be closer to Y.

you can also guess that the coordinates of z will both be negative from the graph. so lets try the coordinate (-2,-12 from your options)

17.88=sqrt(-2-6)^2 + (-12-4)^2
17.88=sqrt (-8)^2 + (-16)^2
17.88= sqrt 64+256
17.88= sqrt320
17.88=17.88
this is a true statement.

D is your answer