Question

The line L has the equation 3x − 4y − 12 = 0.

a) Find the coordinates of the points A and B where the line L crosses the coordinate axes.
b) Find the area of triangle OAB where O is the ori

Answer 1

Explanation:

a) To find the coordinates of the points where the line L crosses the coordinate axes, we can set one of the coordinates to 0 and solve for the other coordinate.

When x = 0 (crosses the y-axis):

3x - 4y - 12 = 0

-4y = 12

y = -3

So, point A is (0, -3).

When y = 0 (crosses the x-axis):

3x - 4y - 12 = 0

3x = 12

x = 4

So, point B is (4, 0).

b) The coordinates of points O, A, and B are (0, 0), (0, -3), and (4, 0) respectively. To find the area of triangle OAB, we can use the formula for the area of a triangle given its vertices:

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Substitute the coordinates of the points:

Area = 0.5 * |0(-3 - 0) + 0(-3 - 0) + 4(0 - (-3))|

= 0.5 * |0 + 0 + 12|

= 0.5 * 12

= 6

So, the area of triangle OAB is 6 square units.