Answer:
The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (5-2)2+(3-8)2
d = √ ((3)2+(-5)2)
d = √ (9+25)
d = √ 34
The distance between the points is 5.8309518948453
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+5)/2=3.5
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(8+3)/2=5.5
The midpoint is: (3.5,5.5)
Graphing the two points, midpoint and distance
P1 (2,8)
P2 (5,3)
Midpoint (3.5,5.5)
The length of the black line is the distance between the points (5.8309518948453)
Find the slope of the line connecting the two points
Slope = (Y2-Y1) = (3-8) = (-5) = -1.66666666666667
(X2-X1) (5-2) (3)
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 -1.66666666666667
y = -1.67x + b
We substitute x and y for the values from one of our points (2,8)
8 = -1.67×2 + b
8 = -3.33 + b
8--3.33 = b
11.33 = b
Knowing both b and m, we can contruct the equation of the line
y= -1.67x+ 11.33
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= -1.67x+ 11.33
0= -1.67x+ 11.33
1.67x= 11.33
x= 11.33/1.67 = 6.80
The x intercept for this straight line is 6.80
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= -1.67×0+ 11.33
y= 11.33
The y intercept for this straight line is 6.80
References
refernce image showing the distance between two points on the xy plane
Step-by-step explanation:
