Finding the distance, midpoint, slope, equation and the x y-interceptsof a line passing between the two points p1 (4,-2) and p2 (-9,-9)The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)d = √(-9-4)2+(-9--2)2d = √((-13)2+(-7)2)
d = √(169+49)
d = √218
The distance between the points is 14.7648230602334
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=(4+-9)/2=-2.5
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(-2+-9)/2=-5.5
The midpoint is: (-2.5,-5.5)
Graphing the two points, midpoint and distance
P1 (4,-2)P2 (-9,-9)Midpoint (-2.5,-5.5)The length of the black line is the distance between the points (14.7648230602334)
Find the slope of the line connecting the two points
Slope = (Y2-Y1) = (-9--2) = (-7) = 0.538461538461538(X2-X1)(-9-4)(-13)Find the equation of the line passing through the two points
The general equation for a straight line isy = mx + bWhere m represents the slope of the line which we found in the previous step to be 0.538461538461538y = 0.54x + bWe substitute x and y for the values from one of our points (4,-2)-2 = .54×4 + b-2 = 2.15 + b-2-2.15 = b-4.15 = bKnowing both b and m, we can contruct the equation of the liney= 0.54x-4.15
X and Y interceptsThe 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= 0.54x-4.150= 0.54x-4.15-0.54x= -4.15x= -4.15/-0.54 = 7.71The x intercept for this straight line is 7.71
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= 0.54×0-4.15y= -4.15The y intercept for this straight line is -4.15
