Shawn connected the four points (-4,1) (-1,4) (5,1) and (-1,-5) on a coordinate plane. Use slope to determine what type of quadrilateral was drawn

Question

You HAVE to use slope to figure out the answer. 

Answer 1

Mark the 4 points on your graph paper.

 

The general  formula for a line segment is:

y = mx + b, where m is the slope, and b is the offset.

 

You can also find the slope of a line using:

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

 

Let's use the 2nd equation on the 2 points in the 2nd quadrant (upper left).  Note that we are finding the slope FROM x1 TO x2

 

m = (-1 - (-4)) / (4 - 1) =  3/3 = 1

 

repeat the procedure for the other 2 points, and you will see that the slope is the same.  thus, you have now identified 2 parallel lines.

 

By inspection, we can see that the other two lines are NOT parallel.  therefore, we do NOT have a parallelogram.

 

Look in your course material --or online-- to see if there is a method to test for a trapezoid using slopes.

Answer 2

Let's start by labeling the points: 

 

A (-4, 1); B (-1,4); C (5,1); D (-1.-5)  

 

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

 

The slope from A to B: (4 - 1)/ (-1 -(-4)) = 3/ (-1 + 4) = 3/3 = 1

 

The slope from B to C: (1- 4)/ (5 -(-1)) =  3/ (5+1) = 3/6 = 1/2

 

The slope from C to D: (- 5 - 1)/ (-1 - 5) = (-6)/(-6) = 1

 

The slope from D to A: (1 -(-5))/ (-4-(-1)) = (1+5)/(-4 +1) = 6/(-3) = -2

 

We now know that line AB and Line CD are parallel. 

 

BC and DA are perpendicular, so we know it isn't a rhombus, parallelogram or square. 

 

Distance = √((x1-x2)^2) + ((y1-y2)^2)

 

We can find the distance between BC: √((-1-5)^2 + (4-1)^2) = √(36 + 9) = √(45) or 3 √(5)

 

DA : ((-1-(-4)^2 + (-5-1)^2) = √((-1 +4)^2 + 36) = √ (9+36) = √(45) or 3 √(5)

 

Because DA and BC have the same length, and AB and CD are parallel, we know ABCD is a trapezoid.