Question

Line segment LM in the coordinate plane has endpoints with coordinates (-8, 13) & (6, -8). Find 2 possible locations for a point P that divides LM into two parts with lengths in a ratio of 6:1.

Answer 1

Answer:

• (4,-5)

,

• (-6,10)

Explanation:

The coordinates of the endpoints of the line segment LM are (-8, 13) and (6, -8).

If point P divides LM into two parts with lengths in a ratio of 6:1.

Since the exact points, L and M are not given, we can switch the coordinates as desired.

• Taking L(-8, 13) and M(6, -8).

$\begin{gathered} P(x,y)=\mleft(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\mright) \\ =(\dfrac{6(6)+1(-8)}{6+1},\dfrac{6(-8)+1(13)}{6+1}) \\ =(\dfrac{36-8}{7},\dfrac{-48+13}{7}) \\ =(\dfrac{28}{7},\dfrac{-35}{7}) \\ P(x,y)=(4,-5) \end{gathered}$

• Taking L(6, -8) and M(-8, 13)

$\begin{gathered} P(x,y)=\mleft(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\mright) \\ =(\dfrac{6(-8)+1(6)}{6+1},\dfrac{6(13)+1(-8)}{6+1}) \\ =(\dfrac{-48+6}{7},\dfrac{78-8}{7}) \\ =(\dfrac{-42}{7},\dfrac{70}{7}) \\ P(x,y)=(-6,10) \end{gathered}$

The two possible locations for point P are (4, -5) and (-6, 10).