Question

C 0The midpoint of a segment can be found using the formulas for a directed line segment, x = ( 2 4 m )(x2 – x3] + xị andy=(a b]W2 - Yd) + y2. When using these formulas to find a midpoint, which is true?a = 1 and b = 2O a = 2 and b = 1O a = 1 and a + b = 2a = 2 and a + b = 2Mark this andenSave and ExitNexSubmit

Answer 1

We know that the mid point formula is

`x=(x_2+x_1)/(2)\text{and y=}(y_2+y_1)/(2)`

we will check one by one which option make this formula by substituing values given:-

It is given that

`x=(a)/(a+b)(x_2-x_1)+x_1and\text{ y=}(a)/(a+b)(y_2-y_1)+y_1`

Now when a=1 anf b=2 we have

`\begin{gathered} x=(1)/(3)(x_2-x_1)+x_1 \\ =(x_2-x_1+3x_1)/(3) \\ =(x_2+2x_1)/(3) \end{gathered}`

which is not the midpoint formula

Now let's substitute a=1 and a+b=2

`\begin{gathered} x=(1)/(2)(x_2-x_1)+x_1 \\ =(x_2-x_1+2x_1)/(2) \\ =(x_2+x_1)/(2) \\ \text{and } \\ y=(1)/(2)(y_2-y_1)+y_1 \\ =(y_2-y_1+2y_1)/(2) \\ =(y_2+y_1)/(2) \end{gathered}`

which is the required formula.

Hence the correct option is a=1 , a+b=2