Question

Based on the coordinates above what kind of quadrilateral wil be formed by their route? How do you know?

Answer 1

Rectangular route

Explanation:

Given

H(-4, 3) B (2, 11) F (6, 8) C (0, 0)

Required

The type of route

First, calculate the distance between adjacent points i.e. HB, BF, FC and CH

Where

HB and FC are opposite

BF and CH are opposite

Using distance formula:

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)`

So, we have:

HB

`H =(-4, 3) \to (x_1,y_1)`

`B = (2, 11) \to (x_2,y_2)`

`HB = √((-4- 2)^2 + (3 -11)^2)= √((-6)^2 + (-8)^2) = √(36 + 64) = √(100) = 10`

BF

`B = (2, 11) \to (x_1,y_1)`

`F = (6, 8) \to (x_2,y_2)`

`BF = √((2- 6)^2 + (11 -8)^2)= √((-4)^2 + (3)^2) = √(16 + 9) = √(25) = 5`

FC

`F = (6, 8) \to (x_1,y_1)`

`C =(0, 0) \to (x_2,y_2)`

`FC = √((6- 0)^2 + (8 -0)^2)= √((6)^2 + (8)^2) = √(36 + 64) = √(100) = 10`

CH

`C =(0, 0) \to (x_1,y_1)`

`H =(-4, 3) \to (x_2,y_2)`

`CH = √((0-- 4)^2 + (0 -3)^2)= √((4)^2 + (-3)^2) = √(16 + 9) = √(25) = 5`

So, we have:

`HB = FC = 10`

`BF = CF = 5`

Sine the opposite sides are equal; We can conclude that the route is a rectangle