Answer:
4
Step-by-step explanation:
Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (-3,6) and p2 (3,2)
The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (3--3)2+(2-6)2
d = √ ((6)2+(-4)2)
d = √ (36+16)
d = √ 52
The distance between the points is 7.21110255092798
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=(-3+3)/2=0
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(6+2)/2=4
The midpoint is: (0,4)
Graphing the two points, midpoint and distance
P1 (-3,6)
P2 (3,2)
Midpoint (0,4)
The length of the black line is the distance between the points (7.21110255092798)
Find the slope of the line connecting the two points
Slope = (Y2-Y1) = (2-6) = (-4) = -0.666666666666667
(X2-X1) (3--3) (6)
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 -0.666666666666667
y = -0.67x + b
We substitute x and y for the values from one of our points (-3,6)
6 = -.67×-3 + b
6 = 2.00 + b
6-2.00 = b
4.00 = b
Knowing both b and m, we can contruct the equation of the line
y= -0.67x+ 4.00
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= -0.67x+ 4.00
0= -0.67x+ 4.00
0.67x= 4.00
x= 4.00/0.67 = 6.00
The x intercept for this straight line is 6.00
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= -0.67×0+ 4.00
y= 4.00
