SOLUTION: The point B(1,2) is one tenth of the way from the point A(-3,4) to the point P(x,y). Find x and y.

Question 853220: The point B(1,2) is one tenth of the way from the point A(-3,4) to the point P(x,y). Find x and y.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
. Finding the equation for line AB will give also the line AP, because we want point P to also be on the line.

LINE AB, AP:
;
Applying point-slope form,

.

A general point on line AB or AP or BP, is the variable point, ordered pair (x, -(3/5)x+13/5).

You can use the Distance Formula to complete the proportion shown at the top of this posting and it will be in ONE unknown variable, x. It may give two solutions, and one of them will be the answer you want and the other will not be the answer you want. You might like to try this process yourself, so I am not showing the rest of that process (yet).
RELATED QUESTIONS
Find the coordinates of point P that is 1/3 of the way from A(4,-3) to B(1,3). Write your (answered by Alan3354)

A point P(x,y) moves in such a way that its distance from (3,2) is always one half of its (answered by josgarithmetic,ikleyn)

The Point P(2,y) equidistant from point F(3,0) and the line with equation x=-3/2. What... (answered by josgarithmetic,ikleyn)

In triangle ABC, point X is the midpoint of line AC and Y is the point one-third of the... (answered by robertb)

Given the following function in two variables x and y f(x, y) = x^3y+2x^4+y^5 a. Find... (answered by parmen)

If the focci of ellipse is {{{ x^2/9 + y^2/4 = 1 }}} subtend a right angle at some point... (answered by ikleyn)

Find the equation that is satisfied by the coordinates of each point. A rod PQ of the... (answered by Fombitz)

Find a distance from the point P(3,5) to the line x= -2 Or Find the distance from... (answered by stanbon)

Point X is located at (2, −6) and point Z is located at (0, 5). Find the y value... (answered by stanbon)