Let AB be the directed line segment beginning at point A(5 , 5) and ending at point B(19 , 16). Find the point P on the line segment that partitions the line segment into the segments AP and PB at a ratio of 5:2.

(9, 57/7)

Step-by-step explanation:

Given the coordinates A(5 , 5)  and B(19 , 16), divided by the point P in the ratio 5:2, to get the coordinate of P, we will use the formula;

P(X, Y) = {{ax1+bx2/a+b, ay1+by2/a+b}

X = ax1+bx2/a+b

Substitute the given values

X = 5(5)+2(19)/5+2

X = 25+38/7

X = 63/7

X = 9

Similarly;

Y = 5(5)+2(16)/5+2

Y = 25+32/7

Y = 57/7

Hence the coordinate of point P is (9, 57/7)

the first one, all those points on the line just make a strait line.