1.. The line with gradient -2 passing through the point P(3t ,2t)intersects the x-axis at A and the y-axis at B.
i Find the area of triangle AOB in terms of t.
The line through P perpendicular to AB intersects the x-axis at C.
ii Show that the mid-point of PC lies on the line y = x

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rebecca7415

09.10.2020

Mathematics

Like you said, we need to use substitution to solve for y.

$x + y = 11\\-1(-x = -y - 9)\\\\x + y = 11\\x = y + 9\\\\y + 9 + y = 11\\\\2y + 9 = 11\\\\2y = 20\\\\y = 10$

Now that we've solved for y, we can plug in the number we got into one of the original equations. (You can choose either equation, but I will use the first one.)

$x + 10 = 11\\\\x = 1$

Now we have the solution of this system.

(1, 10)

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1.. The line with gradient -2 passing through the point P(3t ,2t)intersects the x-axis at A and the y-axis at B. i Find the area of triangle AOB in terms of t. The line through P perpendicular to AB intersects the x-axis at C. ii Show that the mid-point of PC lies on the line y = x