Answer:

frac{y_4-y_3}{x_4-x_3}times frac{y_2-y_1}{x_2-x_1}=-1

Step-by-step explanation:

We know that,

If two line segments are perpendicular then the product of their slope is equal to -1,

Also, the slope of a line segment having the end points (x_n,y_n) and (x_m,y_m) is,

m=frac{y_m-y_n}{x_m-x_n}

So, the slope of line segment AB having end points A(x_1,y_1) and B(x_2,y_2) is,

m_1=frac{y_2-y_1}{x_2-x_1}

Similarly, the slope of line segment CD having end points C(x_3,y_3) and (x_4,y_4) is,

m_2=frac{y_4-y_3}{x_4-x_3}

Hence, by the above property of perpendicular line segments ,

If AB and CD are perpendicular then,

m_1times m_2=-1

implies frac{y_4-y_3}{x_4-x_3}times frac{y_2-y_1}{x_2-x_1}=-1

Third option is correct.