What is the distance between the points (2, 8) and (-6, -7)?

answer:

Step-by-step explanation:Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (2,8) and p2 (-6,-7)

The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula

d = √  ((X2-X1)2+(Y2-Y1)2)

d = √(-6-2)2+(-7-8)2

d = √((-8)2+(-15)2)

d = √(64+225)

d = √289

The distance between the points is 17

The midpoint of two points is given by the formula

Midpoint= ((X1+X2)/2,(Y1+Y2)/2)

Find the x value of the midpoint

Xm=(X1+X2)/2

Xm=(2+-6)/2=-2

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(8+-7)/2=0.5

The midpoint is: (-2,0.5)

Graphing the two points, midpoint and distance

P1 (2,8)

P2 (-6,-7)

Midpoint (-2,0.5)

The length of the black line is the distance between the points (17)

Find the slope of the line connecting the two points

Slope =  (Y2-Y1)  =  (-7-8)  =  (-15)  = 1.875

(X2-X1)(-6-2)(-8)

Find the equation of the line passing through the two points

The general equation for a straight line is

y = mx + b

Where m represents the slope of the line which we found in the previous step to be 1.875

y = 1.88x + b

We substitute x and y for the values from one of our points (2,8)

8 = 1.88×2 + b

8 = 3.75 + b

8-3.75 = b

4.25 = b

Knowing both b and m, we can contruct the equation of the line

y= 1.88x+ 4.25

X and Y intercepts

The x-intercept is a point on the graph where y is zero

Using the equation we found in the previous step and substituting zero for y

y= 1.88x+ 4.25

0= 1.88x+ 4.25

-1.88x= 4.25

x= 4.25/-1.88 = -2.27

The x intercept for this straight line is -2.27

The y-intercept is a point on the graph where x is zero

Using the equation we found in the previous step and substituting zero for x

y= 1.88×0+ 4.25

y= 4.25

The y intercept for this straight line is -2.27