Question

The points −−5, 11 and r, 9 lie on a line with slope 2. Find the missing coordinate r.

Answer 1

`\begin{gathered} Let\text{ }(x_1,y_1),\text{ }(x_2,y_2) \\ Let\text{ }m=slope \\ m=(y_2-y_1)/(x_2-x_1) \end{gathered}`
`\begin{gathered} If(-5,-11)=\text{ }(x_1,y_1),then\text{ }x_1=-5,\text{ }y_1=-11 \\ (r,9)=\text{ }(x_2,y_2),then\text{ }x_2=r,\text{ }y_1=9 \end{gathered}`

Using the Slope formula written above;

`\begin{gathered} 2=(9-(-11))/(r-(-5)) \\ 2=(20)/(r+5) \\ Cross\text{ }multiply \\ 2(r+5)=20 \\ Expansion\text{ }of\text{ }bracket \\ 2r+10=20 \\ 2r=20-10 \\ 2r=10 \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ (2r)/(2)=(10)/(5) \\ r=5 \end{gathered}`

Therefore, the missing co-ordinate r is 5.