Question

Write an equation in slope intercept format of the line that is a segment bisector of both AB and CD. A(-1,8) B(3,4) C(1,10) and D(7,8) find y. ​

Answer 1

Answer:

y = x + 5

Explanation:

The equation of a line in slope intercept form is y = mx + c, where m is the slope and y is the intercept

The midpoint or bisector (x, y) of a line with endpoints at ($x_1,y_1$) and ($x_2,y_2$) is given by:

$x=\frac{x_1+x_2}{2}\\ \\y=\frac{y_1+y_2}{2}$

If AB is at A(-1,8) B(3,4), the coordinates of the midpoint of AB is:

$x=\frac{x_1+x_2}{2}=\frac{-1+3}{2}=1 \\ \\y=\frac{y_1+y_2}{2}=\frac{8+4}{2} =6$

The midpoint of AB is (1, 6)

If CD  is at C(1,10) and D(7,8), the coordinates of the midpoint of CD is:

$x=\frac{x_1+x_2}{2}=\frac{1+7}{2}=4 \\ \\y=\frac{y_1+y_2}{2}=\frac{10+8}{2} = 9$

The midpoint of CD is (4, 9)

The equation of the line passing through two points is given as:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ \\The \ equation \ of\ the\ line \ passing\ through \ the\ midpoint\ of\ AB, i.e (1,6)\ \\and\ the\ mdpoint\ of\ CD\ i.e(4,9)\ is:\\\\y-6=\frac{9-6}{4-1}(x-1)\\ \\y-6=1(x-1)\\\\y=x-1+6\\\\y=x+5$