find the distance and the midpoint between each pair of points with the given coordinates?

A^2 + B^2 = C^2

A= The difference in x-values.

B= The difference in y-values.

C= The distance between the two points.

So, (-4-1)^2 + (9-(-3))^2 = C^2

25 + 144 = C^2

169 = C^2

13 = C

To find the mid-point find the average.

(-4+1)/2 and (9+-3)/2 so the mid-point is. (-1.5,3)

Drop a perpendicular from (-4,9), and draw a line parallel to the x-axis through(1,-3). this gives you a right angled triangle, the sides containing the right angle being 5, (the difference between the x coordinates), and 12, ( the difference between the y coordinates.) Use Pythagoras` Theorem to find the hypotenuse. The mid point will be (-1 1/2, 3). You should be able to see how I got that from the right angled triangle.

Hope this helps, Twiggy.

*you can use this formula in solving the midpoint between each pair of coordinates:

m= X1+X2/2 and

m= Y1+Y2/2

you just have to substitute the given coordinates in that fromula to get the midpoint. For example,

solve for the midpoint of point X:

m= -4 + 1/2

m= -3/2 (this is already simplified so this is the final answer)

solve for the midpoint of point Y:

m= 9 + (-3)/2

m= 9 - 3/2

m= 6/2

m=3

*solving for the distance, you can use ths formula:

d= square root of (x2- x1)^2 + (y2- y1)^2

you just have to substitute the given coordinates in the given formula.

hope this will help.

Given: (-3, 5) & (2, 8) Midpoint: (x, y) = ((-3 + 2)/2, (5 + 8)/2) (x, y) = (-a million/2, 13/2) distance formula: d = sqrt[(x2 - x1)^2 + (y2 - y1)^2] (x1, y1) = (-3, 5) (x2, y2) = (2, 8) d = sqrt[(2 - (-3))^2 + (8 - 5)^2] = sqrt[(5)^2 - (3)^2] = sqrt(25 - 9) = sqrt(sixteen) = 4