Find the coordinates of two more points on the line joining (-1, 4) and (1, 2).
Equation of a straight line two-point form:
y - y1 = ( y2 - y1 ) ( x - x1 ) / ( x2 - x1 )
In this case:
x1 = - 1 , y1 = 4 , x2 = 1 , y2 = 2
y - y1 = ( y2 - y1 ) ( x - x1 ) / ( x2 - x1 )
y - 4 = ( 2 - 4 ) [ x - ( - 1 ) ] / [ 1 - ( - 1) ]
y - 4 = - 2 ( x + 1 ) / ( 1 + 1)
y - 4 = - 2 ( x + 1 ) / 2
y - 4 = - ( x + 1 )
y - 4 = - x - 1
Add 4 to both sides
y = - x - 1 + 4
y = - x + 3
Take any two x coordinates and calculate the y coordinates.
To find the coordinates of two more points on the line joining (-1, 4) and (1, 2), we can use the concept of slope.
1. Calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (-1, 4) and (1, 2), we have:
m = (2 - 4) / (1 - (-1))
= -2 / 2
= -1
2. Once we have the slope, we can find the equation of the line using the point-slope form:
y - y1 = m(x - x1)
Using the point (-1, 4) and the slope -1, we have:
y - 4 = -1(x - (-1))
y - 4 = -1(x + 1)
y - 4 = -x - 1
y = -x + 3
3. Now, we can choose any x-value and calculate the corresponding y-value using the equation of the line. Let's choose x = 0.
Plugging x = 0 into the equation y = -x + 3:
y = -(0) + 3
y = 3
Therefore, one additional point on the line is (0, 3).
4. To find another point, we can choose another x-value, such as x = 2.
Plugging x = 2 into the equation y = -x + 3:
y = -(2) + 3
y = 1
Therefore, another point on the line is (2, 1).
In conclusion, two additional points on the line joining (-1, 4) and (1, 2) are (0, 3) and (2, 1).