Question

For the point P(12,-7) and Q(17,-4), find the

distance d(P,Q) and the coordinates of the midpoint M of
the segment PQ.
C.
What is the distance?
(Simplify your answer. Type an exact
radicals as need.)
What are the coordinates of the midpe
(Simplify your answer. Type an ordere
integers or fractions.)

Answer 1

The distance between points P(12, -7) and Q(17, -4) is √34 units, and the coordinates of the midpoint M are (14.5, -5.5).

Step-by-step explanation:

The question asks us to find the distance d(P,Q) between two points P(12, -7) and Q(17, -4), and the coordinates of the midpoint M of the segment connecting P and Q.

Distance d(P,Q)

To calculate the distance between two points P(x1, y1) and Q(x2, y2) in a Cartesian coordinate system, we use the distance formula:
d(P,Q) = √[(x2 - x1)2 + (y2 - y1)2]

For points P(12, -7) and Q(17, -4):
d(P,Q) = √[(17 - 12)2 + (-4 - (-7))2]

d(P,Q) = √[25 + 9]

d(P,Q) = √[34]

The distance between points P and Q is √34 units.

Coordinates of the Midpoint M

To find the coordinates of the midpoint M between points P(x1, y1) and Q(x2, y2), we calculate the average of the x-coordinates and the average of the y-coordinates:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

For points P(12, -7) and Q(17, -4):

M = ((12 + 17) / 2, (-7 + (-4)) / 2)

M = (29 / 2, -11 / 2)

M = (14.5, -5.5)

The coordinates of the midpoint M are (14.5, -5.5).