salistoun said:Hi all,
How do I go about solving the following question?
Determine whether the points (5 , -6 , 10) and (3, 3 , 8) are on the line
x = 2 + t; y = 3 - 3t, z = 4 + 2t
Stephen
salistoun said:Hi Don,
If I'm correct, the parametric equation for the following points is:
x = -2t + 5, y = -9t - 6 and z = -2t + 10
So no values are matching this parametric
x = 2 + t; y = 3 - 3t, z = 4 + 2t.
So therefore it does not lie on the line right?
To determine if a point (x,y) lies on a line, you can use the slope-intercept form of a line and plug in the x and y values of the point. If the resulting equation is true, then the point lies on the line.
The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
No, a point cannot lie on a vertical line because a vertical line has an undefined slope. This means that for a given x-value, there is no single y-value that can be associated with it.
Yes, there are other ways to determine if a point lies on a line, such as using the point-slope form or the standard form of a line. However, the slope-intercept form is the most commonly used method.
Yes, multiple points can lie on the same line. This is because a line extends infinitely in both directions, so there are infinitely many points that can lie on it.