If A(-7,-3) and B(-2,5), and X between A and B such that AX:XB=1:4, find the coordinates of X.

Question

anonymous · Answer

The point X divides the interval internally.
$$X(\frac{ mx _{2}+mx _{1} }{ m+n }, \frac{ ny _{2}+ny _{1} }{ m+n })$$ where m and n correspond to the ratio given in your question. ie. AX:XB=m:n=1:4. (x1,y1) and (x2, y2) correspond with the points A(-7, -3) and B(-2, 5)
$$X(\frac{ (1)(-7)+(1)(-2) }{ 1+4 }, \frac{ (4)(-3)+(4)(5) }{ 1+4 })$$
$$X(\frac{ -7-2 }{ 5 }, \frac{ -12+20 }{ 5 })$$
$$X(-\frac{ 9 }{ 5 }, \frac{ 8 }{ 5 })$$

anonymous · Answer

$$X(\frac{ mx _{1}+mx _{2} }{ m+n }, \frac{ ny _{1}+ny _{2} }{ m+n })$$ Mixed the numerator up, but it's nothing major because it's basically the same thing.