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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

Respuesta :

We know that the mid point formula is

[tex]x=\frac{x_2+x_1}{2}\text{and y=}\frac{y_2+y_1}{2}[/tex]

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

It is given that

[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1and\text{ y=}\frac{a}{a+b}(y_2-y_1)+y_1[/tex]

Now when a=1 anf b=2 we have

[tex]\begin{gathered} x=\frac{1}{3}(x_2-x_1)+x_1 \\ =\frac{x_2-x_1+3x_1}{3} \\ =\frac{x_2+2x_1}{3} \end{gathered}[/tex]

which is not the midpoint formula

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

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

which is the required formula.

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

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