The diagram shows the $(t,\ x)$ graph for a particle which moves along a straight line. Its first straight section runs from $(0,\ -4)$ to the corner at $(2,\ 2)$ , and A is the point where the graph first crosses the t-axis. Find the coordinates of the point A.

Model answer

(4/3, 0)

Also accepted: (4/3; 0), (4/3 , 0), 4/3, 0, 4/3, (1,33; 0), (1.33, 0), (1 1/3, 0)

Explanation

The first section has gradient

\dfrac{2-(-4)}{2-0}=3

and passes through

(0,\ -4)

, so its equation is

x=3t-4

. It meets the t-axis where

3t-4=0

, that is

t=\dfrac{4}{3}

. So

A\left(\dfrac{4}{3},\ 0\right)

Derived from ZIMSEC Mathematics 9164/4 Paper 4, November 2004, Q12

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