What’s a relationship in geometry?

Question

D is (1,5) E is (7,-3) F is (4,1) and G is (12,7)

Determine the relationships between DE and FG. (With a line above DE and a line above FG).

Answer 1

Hi Shelly!

Good question -- a relationship in geometry, in this case, is just referring to how these two line segments (that's what the line over DE and FG are indicating) are related to each other -- since we're working in 2-dimensional space, the two lines could either intersect at a particular point, be parallel to each other, or be perpendicular to each other.

The easiest way to take a look at this is to graph them out, and what I see is two lines that are pretty close to perpendicular to each other, but we should confirm that by checking their slopes! Remember, perpendicular lines (or orthogonal), will have negative inverse slopes of each other.

Let's use the slope equation to figure out DE:

y2 - y1 / x2 - x1 = m

(-3 - 5) / (7 - 1) = m

m = -8/6, which reduces to -4/3

Now for FG:

(7 - 1) / (12 - 4) = m

m = 8/6, which reduces to 3/4

So we know that the slopes of the two lines are negative inverses of each other, making them orthogonal!

Answer 2

Hi Shelly,

A relationship can be most anything. Often, in math, the word relationship refers to a pairing of numbers that may or may not satisfy the criteria of a function. Here, however, I would be looking for some type of geometric relationship: are the segments parallel or perpendicular (check the slopes of the segments), are they congruent (check the lengths).