Question

Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of ¯¯¯¯¯¯ P Q.

P(3, 2), Q(6, 6)
a. (PQ) ≈ 4.2, Midpoint (x, y) ≈ (4.5, 4)
b. (PQ) ≈ 3.6, Midpoint (x, y) ≈ (4.3, 4.2)
c. (PQ) ≈ 4.6, Midpoint (x, y) ≈ (4.8, 3.8)
d. (PQ) ≈ 4.0, Midpoint (x, y) ≈ (4.0, 4.0)

Answer 1

To find the distance between two points P(3, 2) and Q(6, 6), we can use the distance formula. The distance is approximately 5.0 units. To find the midpoint of PQ, we can use the midpoint formula. The coordinates of the midpoint are (4.5, 4).

Step-by-step explanation:

To find the distance between two points in a plane, we can use the distance formula:

d = √(x2 - x1)^2 + (y2 - y1)^2

For point P(3, 2) and Q(6, 6), we can plug in the values and calculate:

d = √(6 - 3)^2 + (6 - 2)^2

d = √3^2 + 4^2

d = √9 + 16

d = √25

d ≈ 5.0

Therefore, the distance PQ is approximately 5.0 units.

To find the midpoint of PQ, we can use the midpoint formula:

Midpoint (x, y) = ((x1 + x2)/2, (y1 + y2)/2)

For point P(3, 2) and Q(6, 6), we can plug in the values and calculate:

Midpoint (x, y) = ((3 + 6)/2, (2 + 6)/2)

Midpoint (x, y) = (4.5, 4)

Therefore, the coordinates of the midpoint of PQ are (4.5, 4).