Question

Line & is shown in the coordinate plane. y 10 D 9 op 7 6 C с 5 3 2 국 1 A B 2 3 4 5 6 7 8 10 1. What are the coordinates of B and D? 2. Is the point (16, 20) on line (? Explain how you know. 3. Is the point (20,24) on line l? Explain how you know. 4. Is the point (80, 100) on line l? Explain how you know. 5. Write a rule that would allow you to test whether (x, y) is on line l.

Answer 1

the coordinate of B is (4,0)

and D is (8, 10)

the coordinate of C is (4,5) and D is (8, 10)

so the equation of the line passing through two-point is given as follows,

$\begin{gathered} y-4=\frac{10-5}{8-4}(x-5) \\ y-4=\frac{5}{4}(x-5) \\ \end{gathered}$

for point (16, 20)

substitute the value of x and y in the above expression

$\begin{gathered} 20-4=\frac{5}{4}(16-5) \\ 16\ne\frac{55}{4} \end{gathered}$

so it is not satisfying the equation of the line that means the point does not lie on this line