Question

The following set of coordinates represents which figure? (7, 10), (4, 7), (6, 5), (9, 8) Parallelogram Rectangle Rhombus Square

Answer 1

Answer:

The figure is a rectangle

Step-by-step explanation:

* Lets explain how to solve the problem

- To prove the following set of coordinates represents which figure

  lets find the distance between each two points and the slopes of

  the lines joining these points

- The rule of the distance between two point is

 $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

- The rule of the slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- Remember:

* Parallel lines have same slopes

* The product of the slopes of the perpendicular lines is -1

# points (7 , 10) and (4 , 7)

∵ $d1=\sqrt{(4-7)^{2}+(7-10)^{2}}=\sqrt{18}$

∵ $m1=\frac{7-10}{4-7}=\frac{-3}{-3}=1$

# points (4 , 7) and (6 , 5)

∵ $d2=\sqrt{(6-4)^{2}+(5-7)^{2}}=\sqrt{8}$

∵ $m2=\frac{5-7}{6-4}=\frac{-2}{2}=-1$

# points (6 , 5) and (9 , 8)

∵ $d3=\sqrt{(9-6)^{2}+(8-5)^{2}}=\sqrt{18}$

∵ $m3=\frac{8-5}{9-6}=\frac{3}{3}=1$

# points (9 , 8) and (7 , 10)

∵ $d4=\sqrt{(7-9)^{2}+(10-8)^{2}}=\sqrt{8}$

∵ $m4=\frac{10-8}{7-9}=\frac{2}{-2}=-1$

∵ d1 = d3 = √18 and d2 = d4 = √8

∴ Each two opposite sides are equal

∵ m1 = m3 = 1 and m2 = m4 = -1

∴ Each two opposite sides are parallel

∵ m1 × m2 = 1 × -1 = -1

∵ m2 × m3 = 1 × -1 = -1

∵ m3 × m4 = 1 × -1 = -1

∵ m4 × m1 = 1 × -1 = -1

∴ Each two adjacent sides are perpendicular

- The set of coordinates represents a figure has these properties:

1. Each two opposite sides are equal

2. Each two opposite sides are parallel

3. Each two adjacent sides are perpendicular

∴ The figure is a rectangle