Question

Segment AB with endpoints at A(6, 5) and B(6, 15) is partitioned by point P according to the ratio of 3:2. Find the coordinate of point P.Group of answer choices(6, 11)(6, 10)(6, 12)(6, 9)

Answer 1

Soltuion

Step 1:

A(6, 5) and B(6, 15)

Step 2

Write the formula for the division of line segment into ratio a:b

`\begin{gathered} Coordinates\text{ of a point that divide a line segemnt into ratio a:b} \\ =\text{ \lparen}(bx_1+ax_2)/(a+b)\text{ , }(by_1+ay_2)/(a+b)\text{ \rparen} \end{gathered}`

Step 3:

Substitute into the formula to find the coordinates:

a = 3, b = 2

`\begin{gathered} x_1\text{ = 6, y}_1\text{ = 5, x}_2\text{ = 6, y}_2\text{ = 15} \\ \\ =\text{ \lparen }(2*6+3*6)/(3+2)\text{ , }\frac{2*5\text{ + 3}*15}{3+2}) \\ \\ =\text{ \lparen}(12+18)/(5)\text{ , }\frac{10\text{ + 45}}{5}\text{ \rparen} \\ \\ =\text{ \lparen }(30)/(5)\text{ , }(55)/(5)\text{ \rparen} \\ \\ =\text{ \lparen 6 , 11\rparen} \end{gathered}`

Final answer

( 6 , 11 )