Question

a(-5,4) and b(11,20). find the mid - point of ab. (-4,12) (-5,-4) (8,7)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-5,y_1 = 4,x_2=11,y_2 = 20$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{-5 + 11}{2}=\frac{6}{2}=3$.

Step3: Calculate y - coordinate of mid - point

$y=\frac{4+20}{2}=\frac{24}{2}=12$.

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-5,y_1 = 4,x_2=-1,y_2 = 20$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{-5+( - 1)}{2}=\frac{-5 - 1}{2}=\frac{-6}{2}=-3$.

Step3: Calculate y - coordinate of mid - point

$y=\frac{4 + 20}{2}=\frac{24}{2}=12$.

Still not among the options. If we assume the points are $A(-5,4)$ and $B( - 11,20)$:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-5,y_1 = 4,x_2=-11,y_2 = 20$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{-5+( - 11)}{2}=\frac{-5-11}{2}=\frac{-16}{2}=-8$.

Step3: Calculate y - coordinate of mid - point

$y=\frac{4 + 20}{2}=\frac{24}{2}=12$.

Still not among the options. If we assume the points are $A(-5,4)$ and $B(11,20)$ and recalculate correctly:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Calculate x - coordinate

$x=\frac{-5 + 11}{2}=\frac{6}{2}=3$.

Step3: Calculate y - coordinate

$y=\frac{4+20}{2}=\frac{24}{2}=12$.

If we assume the points are $A(-5,4)$ and $B(-11,20)$:

Answer:

(3, 12)

It seems there is an error in the provided options as the correct mid - point calculated above is not among them. If we assume there was a typo in the question and the points are $A(-5,4)$ and $B(-1,20)$: