The points A(3;1), B(1;-2) and C(2;3) in a cartesian plane are given.
If CD is parallel to AD with D(t/3;t+1) determine the value of t
slope of cd=slopeof ad
(3-(t+1))/(2-t/3) = (1-(t+1))/(3-t/3)
check that, solve for t.
If CD is parallel to AD, then CD meets AD at D. But parallel lines never meet!
To determine the value of t, we can use the concept of slopes.
First, let's calculate the slope of line AD. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of points A (3, 1) and D (t/3, t+1), we can calculate the slope of line AD:
m_AD = (t + 1 - 1) / (t/3 - 3)
= (t) / (t/3 - 3)
Since CD is parallel to AD, it will have the same slope. Therefore, we can calculate the slope of line CD using the coordinates of points C (2, 3) and D (t/3, t+1):
m_CD = (t + 1 - 3) / (t/3 - 2)
= (t - 2) / (t/3 - 2)
Since CD is parallel to AD, the slopes m_CD and m_AD are equal:
(t - 2) / (t/3 - 2) = (t) / (t/3 - 3)
To solve this equation for t, we can cross-multiply:
(t - 2) * (t/3 - 3) = (t) * (t/3 - 2)
Simplifying this equation will give us the value of t.