In the xy-coordinate plane, the coordinates of point of point s are (-2, -6), and the coordinates of point t are (18, 9). point q lies on line segment st so that the ratio of the distance from point s to point q to the distance from point q to point t is 3 to 5. what are the coordinates of point q? do not round. q (, ) work shown or explanation:

find the distance between S and T

so i distance is ratio o 3:8

3+8=11

25/11=25/11

3*25/11=75/11

8*25/11=200/11

the distance from S to Q is 75/11 and distance rom Q to T is 200/11

if (x,y) is point Q

is a circle made up of points where Q is 75/11 units away from S

if we find the equation of the line ST and find the intersection of the line and this circle, we can ind the point Q

or (-2,-6) and (18,9), slope is (-6-9)/(-2-18)=-15/-20=3/4

y=3/4x+b, if we put (-2,-6) in we get that b=-9/2

y=3/4x-9/2

if we subsitute for y we get

if we solve this by squareing both sides and doing some algebraeic stuff we get 2 points (because the line crosses the circle at 2 points):

(-82/11,-111/11) and (38/11,-21/11)

we have to pick the one between S and T, check the y value

the irst point has a y value of -10.0909 which is below S, so this isn't the point

the 2n point has a vaue of -1.90909 and this is between -6 and 9 so this is the point

Q is

50

step-by-step explanation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb