Rectangle ABCD has vertices at A(−3,1),B(−2,−1),C(2,1), and D(1,3). What is the area, in square units, of this rectangle?

A

5

B

10

C

25

D

100

B.  10

Step-by-step explanation:

To find the area of this rectangle, we will simply find the distance AB and then find the distance BC, then multiply both together.

First, we will find the distance AB

A(-3,1),      B(-2, -1)

Using the distance formula;

|AB| = √(x₂ - x₁)² + (y₂ - y₁)²

x₁= -3               y₁ = 1                     x₂ = -2                   y₂ = -1

|AB| = √(-2 + 3)² + (-1 - 1)²

        =√(1)² + (-2)²

       = √1 + 4

        = √5

Next, we will find the distance BC

B(-2, -1)          C(2, 1)

Using the distance formula;

|BC| = √(x₂ - x₁)² + (y₂ - y₁)²

x₁= -2               y₁ =- 1                     x₂ = 2                   y₂ = 1

|AB| = √(2 + 2)² + (-1 - 1)²

        =√(4)² + (-2)²

       = √16 + 4

        = √20

Area of the rectangle ABCD = |AB| . |BC|

                                                =  √5 × √20

                                                 = √5×20

                                                   =√100

                                                    =10

Area of the rectangle ABCD  =  10 square units

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.