The coordinates of the point 3/10(3:10) of the way from A(-4, -7) to B(12, 5) are (4/5, -17/5). The division of line segment by a ratio formula is used for calculating the required coordinates of the point P.
A point P divides the line segment AB in the ratio AP: PB (internally). Then the coordinates of the point P are calculated by the formula for ratio a: a+b is
[tex]P(x, y) = (\frac{(bx1+ax2)}{(a+b)} , \frac{(by1+ay2)}{(a+b)})[/tex]
where A(x1, y1); B(x2, y2)
It is given that,
A(-4, -7); B(12, 5) and ratio is 3: 10 = 3: 3+7; so, a = 3 and b = 7
Then the coordinates of the point P(x, y) that is 3/10 of the way from A and B are:
P(x, y) = [tex](\frac{7(-4)+3(12)}{3+7}, \frac{7(-7)+3(5)}{3+7})[/tex]
= [tex](\frac{-28+36}{10},\frac{-49+15}{10})[/tex]
= (8/10, -34/10)
= (4/5, -17/5)
Thus, the required coordinates of the point 3/10 of the way from A to B is P(4/5, -17/5).
Learn more about the division of a line segment here:
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