math problem help

35th qn answer is a can someone explain?

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@LV98xx First you should draw the line that passes through the midpoints of AE and CD (this is parallel to the horizontal sides of the rectangle). Then point F is the reflection of B about this line, so basically F is the point such that CBFD is a rectangle.

It’s asking for the distance from the intersection of BD and CF, to the line AC. BD and CF are just diagonals of rectangle CBFD so this intersection point is easy to construct. It is 15/2 = 7.5 in away from AC.

thank you!

@MITer94 can you please explain this one too answer is j

Each of the following determines a unique plane in 3-dimensional Euclidean space EXCEPT:
F) 1 line and 1 point NOT on the line
G) 2 distinct parallel lines
H) 2 intersecting perpendicular lines
J) 2 lines intersecting in more than 1 point
K) 3 distinct points NOT on the same line

@LV98xx two lines intersect at more than one point (in the standard Euclidean 3D space) if and only if they are the same line. They don’t determine a unique plane.

All other choices determine a unique plane.