Question

The points 6, r and 18, 15 lie on a line with slope 3/2. Find the missing coordinate r.

Answer 1

`\begin{gathered} Let\text{ }m\text{ }be\text{ }the\text{ }slope\text{ }of\text{ }a\text{ }line\text{ }joining\text{ }two\text{ }points\text{ }(x_(1,)y_1)\text{ }and\text{ }(x_(2,)y_2) \\ then\text{ }m=(y_2-y_1)/(x_2-x_1) \end{gathered}`
`\begin{gathered} Let\text{ }(x_(1,)y_1)=(6_,r)\text{ }and\text{ }(x_(2,)y_2)=(18_,15),m=(3)/(2) \\ Using\text{ }the\text{ }above\text{ }formula \\ (3)/(2)=(15-r)/(18-6) \\ (3)/(2)=(15-r)/(12) \\ Cross\text{ }multiply \\ 2(15-r)=3(12) \\ 30-2r=36 \\ -2r=36-30 \\ -2r=6 \\ (-2r)/(-2)=(6)/(-2) \\ r=-3 \end{gathered}`

Therefore, the missing Co-ordinate r = -3