Question

please help!!!! will give medal

9. The vertices of quadrilateral JKLM are J (-2,4); K(-3,-1); L(2,-2); and M(3,3). Find each of the following to show that JKLM is a square. Draw figure.

Answer 1

Part A. Line JM=____; Line ML=____; Line LK=____; Line KM=____

Part B. Slope of Line JM=______ Slope of Line ML=_____

Slope of Line LK=______ Slope of Line KM=_____

Answer 2

that is what i need to know please help

Answer 3

@AkashdeepDeb

Answer 4

@agent0smith

Answer 5

@thomaster

Answer 6

Part A:

This part can be solved by using the distance formula for each points.
The distance formula finds the distance between 2 points:
For eg. if the points are, \((x_1,y_1)\),\((x_2,y_2)\) then the distance between the points would be =

\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Now in the case of a square we'd see that all the sides are of the same length.
ie: JM = ML = KM = LK = some value.

But this information is not enough to prove it a square, we can even infer that this is a rhombus. So we need the next part.

Part B:

In this part you need to find the slope of each line segment.
To find slope we use a simple method = RISE/RUN
For eg. if the points are, \((x_1,y_1)\),\((x_2,y_2)\) then the slope of the line =

Slope = \[\frac{y_2-y_1}{x_2-x_1}\]

So when you have all the slopes, you'd see that there'd be two pairs with the same slope showing that they are parallel and the slopes of the adjacent sides would be negative reciprocals of each other showing that they are perpendicular. Ant thus, we can prove that the sides are perpendicular, equal and parallel to each other and hence it is a square.

Understood? :D