Question

Can anyone help me with this please thank you

Answer 1

Q1 - The length of the side AC is: 12

Q2 - Hence, the distance in kilometers from the courthouse to the library is 12

Q3 - The distance in kilometers, from the courthouse to the bus station is: 15

Q4 - The length of side AB is 3

Q5 - The length of side AD is: 9

Explanation:

Question1:

7 - (-5) = 7 + 5

• Simplify:

12

• Calculate the difference in y - coordinates:

2 - 2

• Simplify:

0

• Apply the distance formula:

AC = √ (12)^2 + (0)^2

• Simplify:

AC = √ 144

• Calculate the square root:

AC = 12

Question 2:

• Make a plan:

In this question, we need to use the distance formula to calculate the distance between the courthouse and the library.

• Solve the problem:

The distance formula is: √ (x2 - x1)^2 + (y2 - y1)^2

The coordinates of the library are ( -5, 2) and the coordinates of the courthouse are (7, 2)

We can substitute these values into the distance formula to get:

√ (7 - (-5))^2 + (2 - 2)^2 = √ 12^2 = 12

Hence, the distance in kilometers from the courthouse to the library is 12

Question 3:

• Make a plan:

In this question we need to use the distance formula to calculate the distance between the courthouse and the bus station:

• Solve the problem:

The distance formula: √ (x2 - x1)^2 + (y2 - y1)^2

The coordinates of the courthouse are (7, 3) and the coordinates of the bus station are ( -8, 3)

• However, the distance between the courthouse and the bus station is:

√ ( -8, - 7)^2 + (3 - 3)^2 = √ 225 = 15

• Draw the conclusion:

The distance in kilometers, from the courthouse to the bus station is: 15

Question 4:

• Write the distance formula:

√(x2 - x1)^2 + (y2 - y1)^2

• Substitute:

(-4, 3) and (-4, 6) into √(x2 - x1)^2 + (y2 - y1)^2

√(-4 + 4)^2 + (6 - 3)^2

• Calculate:

√(-4 + 4)^2 + (6 - 3)^2

• Simplify:

√0^2 + (6 - 3)^2

• Calculate:

√3^2

• Simplify Radical expression:

The length of side AB is: 3

Question 5:

• Calculate the difference in x -coordinates:

( - 2) - (7) = - 9

• Calculate the difference in y - coordinates:

(2) - (2) = 0

AD = √ ( -9)^2 + (0)^2

• Simplify:

AD = √ 81

• Calculate square root:

AD = 9

• Draw a conclusion:

The length of side AD is: 9

Hope this helps!