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

• (4,-5)

,

• (-6,10)

Step-by-step 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((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\mright) \\ =((6(6)+1(-8))/(6+1),(6(-8)+1(13))/(6+1)) \\ =((36-8)/(7),(-48+13)/(7)) \\ =((28)/(7),(-35)/(7)) \\ P(x,y)=(4,-5) \end{gathered}`

• Taking L(6, -8) and M(-8, 13)

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

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