A (7, 4) and B (2, 0), The point C has coordinates (2, t), where t 0, and AC = AB. (a) Find the value of t. (1) (b) Find the area of triangle ABC.

Step 1: Locate the coordinates of the endpoints.
EXAMPLE: The two endpoints M (2, 1) and N (6, 4). Therefore,
(x_1, y_1) = (2, 1) and (x_2, y_2) = (6, 4).
Step 2: Find the length of AC and AB
Step 1: Locate the coordinates of the endpoints.
EXAMPLE: The two endpoints M (2, 1) and N (6, 4). Therefore, (x_1, y_1) =
(2, 1) and (x_2, y_2) = (6, 4).
Step 2: Plug the corresponding coordinates into the Distance Formula. .
FORMULA:
d = \sqrt{(x_2 - x_2)^2 + (y_2 -y_1)^2}
EXAMPLE: Endpoints M (2, 1) and N (6, 4).
d = \sqrt{(6 - 2)^2 + (4 - 1)^2}
Step 3: Calculate the subtraction in parentheses.
Step 4: Square the value in parentheses.
Step 5: Add the numbers under the radical sign.
Step 3: Substitute the either lengths in the given condition
EXAMPLE: A (7, 4) and B (2, 0), The point C has coordinates (2, t), to find t
We can find the t value by this condition AC = AB
Step 4: Simplify the equation to find the unknown variable
NOTE: Apply the BODMAS rules