Jimmy wants to rewrite the set of parametric equations x = 1/2 T + 3 and y = 2T - 1 in rectangular form by eliminating T. Which of the following equations would help him to eliminate T.
A) t = 2(x-3)
B) t = 2(x+3)
C) t = y-1 / 2
D) t = 2(y+1)
Im just doing corrections so i can understand how to properly do it Reiny
Then post your attempts.
my answer is A
correct
To eliminate the parameter T and rewrite the given parametric equations in rectangular form, we need to express T in terms of x and y. Let's examine the options provided:
A) t = 2(x-3)
This equation does not help us eliminate T because it relates T to x directly, not allowing us to express T in terms of x and y.
B) t = 2(x+3)
Similar to option A, this equation also does not help in eliminating T. It relates T only to x, not y.
C) t = (y-1) / 2
This equation allows us to express T in terms of y. We can solve this equation for T by multiplying both sides by 2:
2t = y - 1
Adding 1 to both sides:
2t + 1 = y
By rearranging the equation, we can express T in terms of y:
T = (y + 1) / 2
So, option C helps us eliminate T.
D) t = 2(y+1)
Similar to options A and B, this equation relates T only to y, not x.
Therefore, the answer is option C: t = (y-1) / 2
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