A straight line through Q(2,3) makes an angle 3pi/4 with the negative direction of the x-axis. If the straight line intersects the line x + y - 7 = 0 at P, find PQ. [Ans: 21 plz answer
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PQ = √2
Step-by-step explanation:
A straight line through Q(2,3) makes an angle 3π/4 with the negative direction of the x-axis
=> angle with +ve x axis = π - 3π/4 = π/4
Slope of line = Tan(π/4) = 1
y = x + c
3 = 2 + c
=> c = 1
=> y = x + 1
x + y - 7 = 0
=y = 7 - x
Equating y
=> x + 1 = 7 - x
=> 2x = 6
=> x = 3
y = 4
P = (3 , 4)
Q = (2 ,3 )
=> PQ = √(3 - 2)² + (4 - 3)² = √2
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