Question

Q3 A (1) Complete the following activity to decide whether the points D(0, 3),
E(1.1) and F(3,-1) are collinear or not.
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Answer 1

Answer:

Let D (0,3) , E(1,1) , F(3,-1)

To show that DEF are collinear, show that F lies on line DE.

Step 1: Solve for the equation of DE.

I’ll use the Slope Intercept Form.

y = mx + b.

Solving for the slope, m = (1 - 3) / (1- 0) = ( - 2 / 1) = -2

y = -2 (x) + b.

Knowing that this line hits D,

3 = -2 ( 0 ) + b

3 = b

b = 3.

Thus, line DE: y = -2 (x) +3

Step 2: Substitute the x and y coordinates of F to check if it lies on the same line.

-1 = -2 (3) +3

-1= -6+3

-1= -3

1=3

this is obviously false. Thus F can’t lie on DE, andD,E,F are not collinear.