Question

Find the coordinates of the point M, of thedistance from Q to P.PICHol(0.8,0.6)(1.2, 4.4)ОООО(-1.2, 2.6)(-1.4, 2.8)

Answer 1

When we want to divide a line drawn through two points P and Q with a ratio m:n, the coordinates of the point M can be given as

`M=((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))_{}`

If

`\begin{gathered} Q\to(x_1,y_1)=(-2,2) \\ P\to(x_2,y_2)=(2,5) \end{gathered}`

The ratio m:n will be 1:4, given that M is located at one-fifth of the distance from Q to P.

Hence, the coordinates are

`M=((\lbrack1*2\rbrack+\lbrack4*-2\rbrack)/(4+1),(\lbrack1*5\rbrack+\lbrack4*2\rbrack)/(4+1))`

Solving, we have

`\begin{gathered} M=((2-8)/(5),(5+8)/(5)) \\ M=(-1.2,2.6) \end{gathered}`

The correct option is the THIRD OPTION.