Question

The following diagram shows two triangles, OBC and OBA, on a set of axes. Point C lies on the $y$-axis, and O is the origin. diagram not to scale B C 0 A 5a. The equation of the line BC is $y = 4$. Write down the coordinates of point C. 5b. The $x$-coordinate of point B is $a$. (i) Write down the coordinates of point B; (ii) Write down the gradient of the line OB. 5c. Point A lies on the $x$-axis and the line AB is perpendicular to line OB. (i) Write down the gradient of line AB. (ii) Show that the equation of the line AB is $4y + ax - a^2 - 16 = 0$. 5d. The area of triangle AOB is three times the area of triangle OBC. Find an expression, in terms of $a$, for (i) the area of triangle OBC; (ii) the $x$-coordinate of point A. 5e. Calculate the value of $a$.

          The following diagram shows two triangles, OBC and OBA, on a set of axes. Point
C lies on the $y$-axis, and O is the origin.
diagram not to scale
B
C
0
A
5a. The equation of the line BC is $y = 4$.
Write down the coordinates of point C.
5b. The $x$-coordinate of point B is $a$.
(i) Write down the coordinates of point B;
(ii) Write down the gradient of the line OB.
5c. Point A lies on the $x$-axis and the line AB is perpendicular to line OB.
(i) Write down the gradient of line AB.
(ii) Show that the equation of the line AB is $4y + ax - a^2 - 16 = 0$.
5d. The area of triangle AOB is three times the area of triangle OBC.
Find an expression, in terms of $a$, for
(i) the area of triangle OBC;
(ii) the $x$-coordinate of point A.
5e. Calculate the value of $a$.

The following diagram shows two triangles, OBC and OBA, on a set of axes. Point
C lies on the y-axis, and O is the origin.
diagram not to scale
B
C
0
A
5a. The equation of the line BC is y = 4.
Write down the coordinates of point C.
5b. The x-coordinate of point B is a.
(i) Write down the coordinates of point B;
(ii) Write down the gradient of the line OB.
5c. Point A lies on the x-axis and the line AB is perpendicular to line OB.
(i) Write down the gradient of line AB.
(ii) Show that the equation of the line AB is 4y + ax - a^2 - 16 = 0.
5d. The area of triangle AOB is three times the area of triangle OBC.
Find an expression, in terms of a, for
(i) the area of triangle OBC;
(ii) the x-coordinate of point A.
5e. Calculate the value of a.

Added by Alvaro A.

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