Answer:
q = 2.5
Step-by-step explanation:
calculate the gradients ( slopes ) m of the 2 lines using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, q ) and (x₂, y₂ ) = (6, 5 )
m = [tex]\frac{5-q}{6-4}[/tex] = [tex]\frac{5-q}{2}[/tex]
repeat with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (4, q )
m = [tex]\frac{q-0}{4-0}[/tex] = [tex]\frac{q}{4}[/tex]
Then
[tex]\frac{5-q}{2}[/tex] = 2 × [tex]\frac{q}{4}[/tex] = [tex]\frac{q}{2}[/tex] ( cross- multiply )
2(5 - q) = 2q
10 - 2q = 2q ( add 2q to both sides )
10 = 4q ( divide both sides by 4 )
2.5 = q
