The point P lies on the line joining A(-2, 3) and B(10, 19) such that AP: PB

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The point P lies on the line joining A(-2, 3) and B(10, 19) such that AP: PB = 1:3.

a. Show that the x-coordinate of P is 1 and find the y-coordinate of P.

b. Find the equation of the line through P which is perpendicular to AB.

The line through P which is perpendicular to AB meets the y-axis at the point Q.

c. Find the area of the triangle AQB.

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