What is the area of the triangle in the diagram?

B.

Step-by-step explanation:

the area of a triangle is

Area = baseline × height / 2

the baseline can be any of the 3 sides.

the height is then the perpendicular connection from the corner point opposite of the chosen line to the chosen line.

in this example the easiest approach would be to pick (x1,y1) to (x2,y1) as baseline, and the height would then be the piece of the y-axis from (0,0) to the baseline.

so, how long is the baseline ?

we need to calculate the difference between the coordinates of both corner points.

we have here an easy case, as both points have the same y value, so we only need to look at the difference in x.

baseline = x2 - x1

and the height is here simply (because of the special case) the difference of the baseline from (0,0) on the y-axis

height = y1

therefore, the area of the triangle is

Area = (x2-x1) × y1 / 2 = 1/2 × y1(x2-x1) = solution B

if the corner points and height are not so nicely aligned with the coordinate axis, then we need to calculate the distances by using Pythagoras to determine the "Hypotenuse" of the triangles created by the differences of the individual coordinates.

in our example

((x1,y1) to (x2,y1))² = (x2-x1)² + (y1-y1)² = (x2-x1)² + 0 = (x2-x1)²

and therefore

(x1,y1) to (x2,y1) = (x2-x1)

and we are back to our original solution.

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step-by-step explanation: