Respuesta :
If we plot the points, we can see which 2 points create the length and the width. Using the distance formula, we can compute for the dimensions.
width = sqrt [(-4 - -3)^2 + (0 – 1)^2] = sqrt (2)
length = sqrt [(-3 - 0)^2 + (1 – -2)^2] = sqrt (18)
Therefore the area is:
Area = length * width
Area = sqrt (2) * sqrt (18)
Area = 6
The area of the rectangle is [tex]\boxed{\bf 6\text{\bf\ square units}}[/tex].
Further explanation:
The area of the rectangle is calculated as follows:
[tex]\boxed{\text{Area}=l\cdot b}[/tex]
Here, [tex]l[/tex] is the length and [tex]b[/tex] is the breadth of the rectangle.
The distance [tex]d[/tex] between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is calculated as follows:
[tex]\boxed{d=\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}}[/tex]
Given:
The vertices of the rectangle are [tex](-4,0),(-3,1),(0,-2)[/tex] and [tex](-1,-3)[/tex].
Calculation:
First we calculate the length and the breadth of the rectangle.
The vertices of the rectangle are [tex](-4,0),(-3,1),(0,-2)[/tex] and [tex](-1,-3)[/tex].
Use the vertices [tex](-4,0)[/tex] and [tex](-3,1)[/tex] to calculate the breadth of the rectangle.
The breadth of the rectangle is calculated by using the distance formula.
The breadth of the rectangle is calculated as follows:
[tex]\begin{aligned}b&=\sqrt{(1-0)^{2}+(-3(-4))^{2}}\\&=\sqrt{1^{2}+1^{2}}\\&=\sqrt{2}\end{aligned}[/tex]
Use the vertices [tex](0,-2)[/tex] and [tex](-3,1)[/tex] to calculate the length of the rectangle.
The length of the rectangle is calculated by using the distance formula.
The length of the rectangle is calculated as follows:
[tex]\begin{aligned}l&=\sqrt{(2-(-1))^{2}+(0-(-3))^{2}}\\&=\sqrt{(-3)^{2}+3^{2]}\\&=\sqrt{9+9}\\&=3\sqrt{2}\end{aligned}[/tex]
The length of the rectangle is [tex]3\sqrt{2}\text{ units}[/tex] and the breadth of the rectangle is [tex]\sqrt{2}\text{ units}[/tex].
Step 2:
The area of the rectangle is calculated as follows:
[tex]\begin{aligned}\text{Area of rectangle}&=l\cdot b\\&=3\sqrt{2}\cdot \sqrt{2}\\&=6\end{aligned}[/tex]
Thus, the area of the rectangle is [tex]6\text{ square units}[/tex].
Therefore, the area of the rectangle is [tex]\boxed{\bf 6\text{\bf\ square units}}[/tex].
Learn more:
1. Learn more about the equation of the circle https://brainly.com/question/1506955
2. Learn more about the angles to define a term https://brainly.com/question/1953744
3. Learn more about the line segment https://brainly.com/question/909890
Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Area and Perimeter
Keywords: Perimeter, area, triangle, rectangle, herons’s formula, distance formula, side, length, width, polygon, coordinate, vertices, algebraic expression, identity, distance formula.
