Final answer:
The value of t for the line joining points (-1,-3) and (1, t) that is perpendicular to a line with gradient 2 is -4.
Step-by-step explanation:
To find the value of t given that the line joining the points (-1,-3) and (1, t) is perpendicular to a line with gradient 2, we must use the concept that the gradients of perpendicular lines are negative reciprocals of each other. Since the given line has a gradient of 2, the line joining (-1,-3) and (1, t) must have a gradient of -1/2.
We can use the formula for the gradient of a line (m) which is given by:
m = (y2 - y1)/(x2 - x1)
Substituting the values of the coordinates into the formula, we get:
-1/2 = (t - (-3))/(1 - (-1))
Now we solve for t:
-1/2 = (t + 3)/2
-1 = t + 3
Therefore, t = -4.