Question

How much longer is CD compared to AB ? Round your solution to 2 decimal points.

Answer 1

Answer:

• Segment CD is 0.66 units longer than segment AB.

Explanation:

Use the distance formula (Pythagoras) between two points to find the length of each segment:

• $length=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

1) Segment AB:

• Coordinates of point A: (-11,4)
• Coordinates of point B: (-8,8)

• $length=\sqrt{(-8-(-11))^2+(8-4)^2}=\sqrt{(3)^2+(4)^2}}=\sqrt{9+16}=\sqrt{25}=5$

2) Segment CD:

• Coordinates of point C: (3,2)

• Coordinates of point D: (7, -2)

• $length=\sqrt{(7-3)^2+(-2-2)^2}=\sqrt{(4)^2+(4)^2}}=\sqrt{16+16}=\sqrt{32}$

3) Difference:

• $\sqrt{32} -5=5.66-5=0.66$

Answer 2

Answer:

CD is 0.66 units longer than AB.

Step-by-step explanation:

Coordinates of A and B are (-11, 4) and (-8, 8)

Therefore, from the formula of distance between two points (x, y) and (x', y')

d = $\sqrt{(x-x')^{2}+(y-y')^{2}}$

Distance AB = $\sqrt{(-11+8)^{2}+(4-8)^{2}}$

AB = $\sqrt{9+16}$

AB = 5

Similarly distance between C (3, 2) and D(7, -2) will be

CD = $\sqrt{(7-3)^{2}+(-2-2)^{2}}$

CD = $\sqrt{32}$

CD = 5.66

Difference between the lengths of AB and CD = 5.66 - 5

= 0.66

Therefore, CD is 0.66 units longer than AB.