Answer:
2.23606797749979
Midpoint
(2,−4.5)
Slope
0.5
x intercept
11.00
y intercept
−5.50
Step-by-step explanation:
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (1-3)2+(-5--4)2
d = √ ((-2)2+(-1)2)
d = √ (4+1)
d = √ 5
The distance between the points is 2.23606797749979
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+1)/2=2
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(-4+-5)/2=-4.5
The midpoint is: (2,-4.5)
Graphing the two points, midpoint and distance
P1 (3,-4)
P2 (1,-5)
Midpoint (2,-4.5)
The length of the black line is the distance between the points (2.23606797749979)
Find the slope of the line connecting the two points
Slope = (Y2-Y1) = (-5--4) = (-1) = 0.5
(X2-X1) (1-3) (-2)
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 0.5
y = 0.50x + b
We substitute x and y for the values from one of our points (3,-4)
-4 = .50×3 + b
-4 = 1.50 + b
-4-1.50 = b
-5.50 = b
Knowing both b and m, we can contruct the equation of the line
y= 0.50x-5.50
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= 0.50x-5.50
0= 0.50x-5.50
-0.50x= -5.50
x= -5.50/-0.50 = 11.00
The x intercept for this straight line is 11.00
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= 0.50×0-5.50
y= -5.50
The y intercept for this straight line is -5.50
