Question

is this figure defined W,X,Y and Z a rhombus? justify your answer

Answer 1

Step 1: Write out the formula for finding the distance d between two points (x1,y1) and (x2,y2)

$\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}$

Step 2: Find the distance between the vertices of the figure

The distance d1 between vertices X(6,-5) and Y(11,-5) is 11-6 = 5 units.

The distance d2 between vertices Y(11,-5) and Z(11,-10) is -5 -- 10 = 5 units.

The distance d3 between vertices Z(11,-10) and W(6,-10) is 11 - 6 = 5 units.

The distance d4 between vertices W(6,-10) and X(6,-5) is -5 -- 10 = 5 units.

Hence all the sides of the figure are congruent

Step 3: Write out the formula for finding the gradient m of the line joining two points (x1,y1) and (x2,y2).

$m=\frac{y_2-y_1}{x_2-x_1}$

Step 4: Check if side XY is Parallel to side WZ

Let m1 be the gradient of XY. Then

$m1=\frac{-5--5}{11-6}=\frac{0}{5}=0_{}$

Let m2 be the gradient of WZ. Then

$m2=\frac{-10--10}{11-6}=\frac{0}{5}=0_{}$

Hence XY is parallel to WZ ( and they are parallel to the x-axis)

Step 5: Check if side XW is Parallel to side YZ

Let m1 be the gradient of XW. Then

$m1=\frac{-10--5}{6-6}=\frac{-5}{0}=\text{undefined}$

Let m2 be the gradient of YZ. Then

$m2=\frac{-10--5}{11-11}=\frac{-5}{0}=\text{ undefined}$

Hence XY is parallel to YZ ( and they are parallel to the y-axis)

Therefore,

WXYZ is a rhombus. Based on the coordinates opposite sides are parallel and all the sides are congruent

The second option