What is the perimeter of the rectangle that results from connecting the following points: left-parenthesis negative 3 comma 1 right-parenthesis, left-parenthesis negative 3 comma 2 right-parenthesis, left-parenthesis 0 comma 2 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis?
A. 8 units
B. 10 units
C. 11 units
D. 12 units
Which of the following points could be added to the graph to create a square? Choose all that apply.
A coordinate grid is shown with two points plotted. Point A is located at left-parenthesis negative 2 comma 3 right-parenthesis. Point B is located at left-parenthesis 3 comma 3 right-parenthesis.
A. left-parenthesis negative 2 comma negative 2 right-parenthesis
B. left parenthesis negative 2 comma negative 3 right parenthesis
C. left parenthesis 3 comma negative 2 right parenthesis
D. left parenthesis 3 comma negative 3 right parenthesis
huh? 3+1+3+1 = 8, not 11!
Oh dear, you are right! I apologize for my mistake. The correct answer is $\boxed{\textbf{(A)}\ 8}$ units.
Since $A$ and $B$ form opposite vertices of a rectangle, we need to plot points such that there are two sides of the rectangle that have length $3-(-2)=5$ units. We can see that adding point $C(3,8)$ will complete the rectangle $ABCD$, which has opposite sides $AB$ and $CD$ with length $5$ units. To make this a square, we need to add a fourth point $E$ such that $ABCE$ is a square. Since $BC$ has length $3-(-2)=5$ units, the distance from $E$ to line $AB$ must also be $5$ units (because $AB$ is a side of the square). Thus, $E$ must be located $5$ units to the left of $AB$ and $5$ units above $B$. Therefore, we have $E(-2,8)$.
The only answer choice that matches this point is $\boxed{\textbf{(A)}\ \text{only}}$.
To find the perimeter of a rectangle, we need to add up the lengths of all four sides. Let's calculate the lengths of the sides using the given points.
The distance between points (x1, y1) and (x2, y2) can be calculated using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the lengths of the four sides:
Side 1: (x1, y1) = (-3, 1) and (x2, y2) = (-3, 2)
d = sqrt((-3 - (-3))^2 + (2 - 1)^2)
= sqrt(0^2 + 1^2)
= sqrt(1)
= 1 unit
Side 2: (x1, y1) = (-3, 2) and (x2, y2) = (0, 2)
d = sqrt((0 - (-3))^2 + (2 - 2)^2)
= sqrt(3^2 + 0^2)
= sqrt(9 + 0)
= sqrt(9)
= 3 units
Side 3: (x1, y1) = (0, 2) and (x2, y2) = (0, 1)
d = sqrt((0 - 0)^2 + (1 - 2)^2)
= sqrt(0^2 + (-1)^2)
= sqrt(0 + 1)
= sqrt(1)
= 1 unit
Side 4: (x1, y1) = (0, 1) and (x2, y2) = (-3, 1)
d = sqrt((-3 - 0)^2 + (1 - 1)^2)
= sqrt(-3^2 + 0^2)
= sqrt(9 + 0)
= sqrt(9)
= 3 units
Adding up the lengths of all four sides:
1 + 3 + 1 + 3 = 8 units
Therefore, the perimeter of the rectangle is 8 units.
The correct answer is A. 8 units.
To find the perimeter of a rectangle, you need to add up the lengths of all its sides. In this case, the rectangle has four sides formed by the given points.
First, let's identify the coordinates of the four points given:
Point A: (-3, 1)
Point B: (-3, 2)
Point C: (0, 2)
Point D: (0, 1)
To calculate the length of each side, you need to find the distance between two points. The distance formula is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Now, let's calculate the length of each side:
1. Side AB:
d_AB = √[(-3 - (-3))^2 + (2 - 1)^2]
= √[0^2 + 1^2]
= √(1)
= 1
2. Side BC:
d_BC = √[(0 - (-3))^2 + (2 - 2)^2]
= √[3^2 + 0^2]
= √(9)
= 3
3. Side CD:
d_CD = √[(0 - 0)^2 + (1 - 2)^2]
= √[0^2 + (-1)^2]
= √(1)
= 1
4. Side DA:
d_DA = √[(-3 - 0)^2 + (1 - 1)^2]
= √[(-3)^2 + 0^2]
= √(9)
= 3
Now, let's find the perimeter by adding up the lengths of all sides:
Perimeter = AB + BC + CD + DA
= 1 + 3 + 1 + 3
= 8 units
Therefore, the perimeter of the rectangle formed by the given points is 8 units. Thus, the correct answer is A.