#### The points A, B and C have coordinates (6, 7), (8, 2) and (0, \frac{23}{5}) and respectively. The line l passes through the point A and is perpendicular to the line AB.

Find the area of ΔOCB, where O is the origin.

Anonymous

0

Find the area of ΔOCB, where O is the origin.

Krishna

0

Method 1:

Step 1: Locate the coordinates of the endpoints.

EXAMPLE: The given points M (2, 3) and N (-1, 0), (2, -4.)

Therefore, (x_1, y_1) = (2, 3),(x_2, y_2) = (-1, 0) and (x_3, y_3) = (2, -4).

Step 2: Plug the corresponding coordinates into the Area of triangle formula

FORMULA:

Area of the triangle

\frac{1}{2} {x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}

Step 3: Simplify further

NOTE: Apply the BODMAS rules

Method 2:

Step 1: Calculate the base and height lengths of the triangle

NOTE: Use the distance formula to calculate lengths.

Step 2: Substitute the either values (base and height lengths) in the formula

Area of the right angle triangle = \frac{1}{2} base * height

Step 3: Simplify further

NOTE: Apply the BODMAS rules