find the distance d (P_1 & P_2) between points P_1 and P_1.

Question

P_1=(-3,3)
P_2=(1,5)

Find the midpoint of the line segment joining the points P_1 and P_2.
P_1=(1,1)
P_2=(-3,3)

Please show all work

Answer 1

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

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

Given the coordinates of the two points, we can plug them into the formula:

P_1 = (-3, 3)
P_2 = (1, 5)

d = sqrt((1 - (-3))^2 + (5 - 3)^2)

d = sqrt((1 + 3)^2 + (5 - 3)^2)

d = sqrt(4^2 + 2^2)

d = sqrt(16 + 4)

d = sqrt(20)

So, the distance between the two points is √20.

Now, to find the midpoint of the line segment joining the two points, we can use the midpoint formula:

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

Given the coordinates of the two points, we can plug them into the formula:

P_1 = (1, 1)
P_2 = (-3, 3)

M = ((1 + (-3))/2, (1 + 3)/2)

M = ((1 - 3)/2, (1 + 3)/2)

M = (-2/2, 4/2)

M = (-1, 2)

So, the midpoint of the line segment joining the two points is (-1, 2).