Question

point a is at (-2.5, -5) and point b is at (5, 10). if point m=(1 - t)a + tb=(-1, -2), what is the value of t? you can use the interactive diagram below to help you :

Explanation:

Step1: Expand the x - coordinate equation

Given $M=(1 - t)A+tB$, for the x - coordinates: $(1 - t)(-2.5)+t(5)=-1$. Expand it: $-2.5 + 2.5t+5t=-1$.

Step2: Combine like - terms

Combine the t terms: $-2.5+(2.5t + 5t)=-1$, so $-2.5 + 7.5t=-1$.

Step3: Isolate the t term

Add 2.5 to both sides: $7.5t=-1 + 2.5$, then $7.5t = 1.5$.

Step4: Solve for t

Divide both sides by 7.5: $t=\frac{1.5}{7.5}=\frac{1}{5}=0.2$.

Answer:

$0.2$