Question

The points F(4,

-2), G(9,
-6), H (8, -1), and I (5, 2) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that BEST identifies the type of
quadrilateral.
(PHOTO BELOW)

Answer 1

see below for slopes and lengths

scalene quadrilateral

Explanation:

When calculations are repetitive, it is reasonable to let a spreadsheet do them.

FG: slope: -4/5, length: √41 ≈ 6.40

GH: slope: -5, length: √26 ≈ 5.10

HI: slope: -1, length: 3√2 ≈ 4.24

IF: slope: 4, length: √17 ≈ 4.12

All of the segments are different lengths, and none of them are parallel or perpendicular. The figure is a scalene quadrilateral.

__

As you know, the slope is calculated from ...

m = (y2 -y1)/(x2 -x1)

and the length is calculated from ...

d = √((x2 -x1)^2 +(y2 -y1)^2)

_____

In the attached spreadsheet, the slope and length are calculated from the point below. That is, the values on the line for F are for segment FG.