b(-4,3),g(-2,4),h(1,-2),l(-1,-3);slope formula

Question

graph each quadrilateral withthe given vertices.

determine whether the figure is a rectangle.

justify your answer using the indicated formula

Answer 1

 

The figure is a rectangle.

Slope between two points (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1).

Two lines are perpendicular if the product of their slopes is -1.

Slopes of BG and LH are the same=(4-3)/(-2-(-4))=1/(-2+4)=½,

and (-2-(-3))/(1-(-1))=(-2+3)/(1+1)=½. So BG||LH.

Slopes of GH and BL are the same:

(-2-4)/(1-(-2))=(-6)/3=(-3-3)/(-1-(-4))=-6/(3)=-2. So GH||BL.

Also, (½)(-2)=-1 which means the pairs of parallels are perpendicular. These define a rectangle.