Question

Please help on 13 and 14

Answer 1

13) The planes ABF and FHG are perpendicular

14) Segments Ab and CD are parallel.

Explanation:

13)

Planes ABF and FHG are perpendicular (they intersect along side EF)

14)

In order to find out about the segments AB and CD, let's use the formula for the slope that joins any two points
`(x_1,y_1)\,\,\&\,\,(x_2,y_2)` on the plane:

`slope=(y_2-y_1)/(x_2-x_1)`

Therefore, given:

A = (-3, 2)

B = (1, 4)

C = (-3, -1)

D = (1, 1)

we have for segment AB the following slope:

`slope_(AB)=(4-2)/(1+3) =(2)/(4) =(1)/(2)`

and for segment CD the following slope:

`slope_(CD)=(1+1)/(1+3) =(2)/(4) =(1)/(2)`

Since they show the same slope, these two segments are parallel.