Question

The coordinates of the endpoints of LM are L(5,17) and M(15,12). Point N is on LM and divides it such that LN:MN is 2:1. Are the coordinates of N?

a) (7,15)
b) (9,14)
c) (11,13)
d) (13,12)

Answer 1

The coordinates of point N that divides LM in the ratio 2:1 do not match any of the provided options when calculated using the section formula.

Step-by-step explanation:

The coordinates of point N, which divides segment LM in the ratio 2:1, can be found using the section formula. Given L(5,17) and M(15,12), we apply the formula (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n), where n:m is the division ratio, L is x1,y1 and M is x2,y2.

Substituting in the given values, we have N = ((1*15 + 2*5)/(1+2), (1*12 + 2*17)/(1+2)), which simplifies to N = (25/3, 46/3). Converting these to whole numbers, we get N = (8.33, 15.33), which when rounded to the nearest whole numbers gives us close to (8, 15), but none of the options match these coordinates. Thus, we conclude a mistake may have occurred in the given options or in the ratio provided.