Question

Charles drew a plan for a rectangular piece of material that hehe will use for a blanket. Three of the vertices are ​( -2.3 and −3.6​), ​(−2.3​, and 2.2​), and ​(2.1​, and 2.2​). What are the coordinates of the fourth​ vertex?

Answer 1

Answer:

The coordinates of the fourth​ vertex is ( 2.1 , -3.6)

Step-by-step explanation:

Given:

The vertices are  ​( -2.3 and −3.6​), ​(−2.3​, and 2.2​), and ​(2.1​, and 2.2​).

To Find :

The fourth coordinate = ?

Solution:

Let (a,b) be the missing coordinates

Now let us use the the mid point formula and find the missing coordinate.

Let  ​( -2.3 ,−3.6​) be the point A

Let  ​​(−2.3​,2.2​) be the point B

Let  ​ ​(2.1​, 2.2​​) be the point C

The mid point of AC should be BD

Step 1: Finding The mid pint of AC

The mid pint of AC

$(\frac{(-2.3+2.1)}{2} , \frac{(-3.6+2.2)}{2})$

$(\frac{(-0.2)}{2} , \frac{(-1.4)}{2})$

$(-0.1, -0.7)$

Step 2: Lets Equate the midpoints'

The mid pint of BD

=>$(\frac{(a+(-2.3))}{2} , \frac{(b+2.2)}{2})$ =  (-0.1, -0.7)

$\frac{(a+(-2.3))}{2} = -0.1$

$(a-2.3) = -0.1 \times 2$

$(a-2.3) = -0.2$

$a = -0.2 +2.3$

a = 2.1

$\frac{(b+2.2)}{2} = -0.7$

$(b+2.2)= -0.7 \times 2$

$(b+2.2)= -1.4$

$b= -1.4 -2.2$

b = -3.6