Question 1

Question

Question 1
A)
Use the image to answer the question.

A straight, solid line connects plotted points E and F on a coordinate plane. The line slopes downward from left to right. Point E is left parenthesis negative 6 comma 1 right parenthesis. Point F is left parenthesis 2 comma negative 5 right parenthesis.

How would you set up the distance formula to find the distance between points E
 and F
.

(1 point)
Responses

d=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√
d is equal to square root of open paren negative 6 minus 2 close paren squared plus open paren 1 minus negative 5 close paren squared end root

d=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 6 minus 2 close paren squared plus open paren 1 minus 5 close paren squared end root

d=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 6 close paren squared plus open paren 5 minus 1 close paren squared end root

d=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√
d is equal to square root of open paren negative 2 plus 6 close paren squared plus open paren 5 plus 1 close paren squared end root
Question 2
A)DaQuan marks two points on the coordinate plane. One point is L(4,2)
 and the other point is M(7,6)
. What is the correct way for DaQuan to set up the distance formula?(1 point)
Responses

d=(4−7)2+(2−6)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 4 minus 7 close paren squared plus open paren 2 minus 6 close paren squared end root

d=(6−7)2+(2−4)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 6 minus 7 close paren squared plus open paren 2 minus 4 close paren squared end root

d=(2−7)2+(4−6)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 7 close paren squared plus open paren 4 minus 6 close paren squared end root

d=(2−4)2+(6−7)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 4 close paren squared plus open paren 6 minus 7 close paren squared end root
Question 3
A)
Use the image to answer the question.

Parallelogram upper A upper B upper C upper D is graphed on a coordinate plane. The x-axis ranges from negative 6 to 6 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 1.

Use the given coordinates to compute the perimeter of the parallelogram.

(1 point)
Responses

25.2 units
25.2 units

26.6 units
26.6 units

28 units
28 units

13.3 units
13.3 units
Question 4
A)
Use the image to answer the question.

Trapezoid upper A upper B upper C upper D is graphed on a coordinate plane. The x-axis ranges from negative 1 to 6 in increments of 1.  The y-axis ranges from negative 1 to 4 in increments of 1.

Use the coordinates to compute the perimeter of the trapezoid. Round each calculation to the nearest tenth.

(1 point)
Responses

12.3 units
12.3 units

16.3 units
16.3 units

14.4 units
14.4 units

13.8 units
13.8 units
Question 5
A)
Use the image to answer the question.

A triangle is graphed on a coordinate plane. The x-axis ranges from negative 2 to 6 in increments of 1. The y-axis ranges from negative 2 to 4 in increments of 1.

Use the coordinates to compute the perimeter of the triangle.

(1 point)
Responses

12 units
12 units

11.2 units
11.2 units

10 units
10 units

10.8 units
10.8 units

GPT-4o mini · Answer

To address your questions, let's go one by one based on the given descriptions of the coordinate points and the geometric figures.

Question 1

Points E (-6, 1) and F (2, -5). We set up the distance formula as follows:

Distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

For points E and F:

\( x_1 = -6 \), \( y_1 = 1 \)
\( x_2 = 2 \), \( y_2 = -5 \)

Substituting these values into the formula: \[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \] This simplifies to: \[ d = \sqrt{(2 + 6)^2 + (-5 - 1)^2} = \sqrt{(8)^2 + (-6)^2} \]

So the correct setup is: Response: \[ d = (2 - (-6))^2 + (-5 - 1)^2 \]

Question 2

Points L (4, 2) and M (7, 6). Setting up the distance formula:

Using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] For points L and M:

\( x_1 = 4 \), \( y_1 = 2 \)
\( x_2 = 7 \), \( y_2 = 6 \)

Substituting these values: \[ d = \sqrt{(7 - 4)^2 + (6 - 2)^2} \]

So the correct setup is: Response: \[ d = (7 - 4)^2 + (6 - 2)^2 \]

Question 3

To compute the perimeter of parallelogram ABCD, you will need to know the lengths of two adjacent sides. If the lengths of the sides were provided in the image, you would sum them appropriately for the final perimeter.

For example, if the lengths of the adjacent sides are \( a \) and \( b \), then: Perimeter = 2(a + b)

You should pick the appropriate response based on the calculations from the image once the side lengths are confirmed.

Question 4

To compute the perimeter of trapezoid ABCD, you need the lengths of all four sides. Again, if those lengths were provided in the image, you would add them up.

For example: Perimeter = AB + BC + CD + DA

Select the option based on the accurate calculations.

Question 5

For the triangle's perimeter, you will similarly need the lengths of each side, calculated using the distance formula for each pair of points.

For a triangle with vertices at A, B, and C: Perimeter = AB + BC + CA

Choose the accurate response once you perform the calculations using the distances derived from the coordinates.

If there are specific answers you need based on particular coordinates or lengths that I am not accounting for, please provide those details so that I can assist you further!