Question

18. Point P divides ABwith A(-4, -5) and B(2, 4)in the ratioof 1:5.Where ispoint Plocated?

Answer 1

Point P divides AB with A(-4,-5) and B(2,4) in a ratio of 1:5.

Therefore, the ratio of 1:5 is also m1= 1 and m2= 5. Then, we must use the following formula:

`\begin{gathered} P=\text{ \lparen}\frac{m1x2+m2x1}{m1\text{ + m2}},\frac{m1y2+m2y1}{m1\text{ + m2}}) \\ \\ P=\text{ \lparen}\frac{\lparen1\lparen2\rparen+5\lparen-4\rparen\rparen}{1\text{ + 5}},\text{ }\frac{\lparen1\lparen4\rparen+5\lparen\text{ -}5\rparen\rparen}{1+\text{ 5}}) \\ \\ P=\text{ \lparen}(\lparen2-20\rparen)/(6),\text{ }\frac{\lparen4\text{ -}25\rparen}{6}) \\ \\ P=\text{ \lparen}(-18)/(6),\text{ }\frac{\text{ -21}}{6}) \\ \\ P=\text{ \lparen-3, -3.5 }) \end{gathered}`

Then, P is located at (-3, -3.5. Answer D.