Question

This question is worth 4 marks

Answer 1

`A(0,\ y_A),\ B(3,\ y_B),\ y=2x+1\\\\\text{put the values of x from the coordinates of the points A and B}\\\text{to the equation of the function, and calculate the values of y}\\\\for\ x=0\to y_A=(2)(0)+1=0+1=1\\for\ x=3\to y_B=(2)(3)+1=6+1=7`

`C(0, y_C),\ D(3,\ y_D),\ y=-x-1\\\\\text{put the values of x from the coordinates of the points C and D}\\\text{to the equation of the function, and calculate the values of y}\\\\for\ x=0\to y_C=-0-1=-1\\for\ x=3\to y_D=-3-1=-4`

`|AC|=|y_C-y_A|\to|AC|=|-1-1|=|-2|=2\\\\|BD|=|y_D-y_B|\to|BD|=|-4-7|=|-11|=11\\\\\boxedBD`