Question

What is the slope-intercept equation that represents a midsegment of the triangle below?

Answer 1

Answer:

$\boxed{\boxed{y=-0.5x+1.75}}$

Step-by-step explanation:

A mid-segment of a triangle is a segment connecting the midpoints of two sides of a triangle.

One mid segment is joining the mid points of EF and FD.

Mid point of ED,

$=(\dfrac{1-4}{2},\dfrac{4+1}{2})$

$=(-1.5,2.5)$

Mid point of EF,

$=(\dfrac{1+2}{2},\dfrac{4-2}{2})$

$=(1.5,1)$

Line joining $(-1.5,2.5)$ and $(1.5,1)$ is,

$\Rightarrow \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}$

$\Rightarrow \dfrac{y-2.5}{1-2.5}=\dfrac{x+1.5}{1.5+1.5}$

$\Rightarrow \dfrac{y-2.5}{-1.5}=\dfrac{x+1.5}{3}$

$\Rightarrow \dfrac{y-2.5}{1}=\dfrac{x+1.5}{-2}$

$\Rightarrow -2(y-2.5)=x+1.5$

$\Rightarrow -2y+5=x+1.5$

$\Rightarrow -2y=x+1.5-5$

$\Rightarrow -2y=x-3.5$

$\Rightarrow y=-\dfrac{1}{2}x+\dfrac{3.5}{2}$

$\Rightarrow y=-0.5x+1.75$

The general point slope formula is,

$y=mx+c$

where,

m = slope, c = y intercept.

So comparing this equation we get,

slope = $-0.5$

y intercept = $1.75$