Question

What are the approximate lengths of the segments AB and CD given the following coordinates:

AB: A(0, 2), B(-3, 8)
CD: C(-2, 2), D(0, -4)

Select the closest approximate lengths:
A) Length of AB is approximately 7.62 units.
B) Length of CD is approximately 6.32 units.

Are the segments congruent? If not, which segment is longer?
C) The segments are congruent.
D) AB is longer.
E) CD is longer.

Answer 1

The approximate lengths of segments AB and CD are 6.71 units and 6.32 units, respectively.

Step-by-step explanation:

To find the lengths of segments AB and CD, we can use the distance formula. The distance formula is given by:

AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For segment AB, the coordinates are A(0, 2) and B(-3, 8). Substituting the values into the distance formula, we get:

AB = sqrt((-3 - 0)^2 + (8 - 2)^2)

AB = sqrt(9 + 36)

AB = sqrt(45)

AB is approximately 6.71 units (rounded to two decimal places).

For segment CD, the coordinates are C(-2, 2) and D(0, -4). Substituting the values into the distance formula, we get:

CD = sqrt((0 - (-2))^2 + (-4 - 2)^2)

CD = sqrt(4 + 36)

CD = sqrt(40)

CD is approximately 6.32 units (rounded to two decimal places).