Question

Help me out please and thank you

Answer 1

Answer: 1

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Step-by-step explanation:

We're given the height in relation to base BC, so we need to find the length of this base. This is the same as finding the distance from B to C.

Turn to the distance formula

`d = \text{Distance from B to C}\\\\d = √((x_1-x_2)^2+(y_1-y^2)^2)\\\\d = √((-2-(-3))^2+(-1-(-2))^2)\\\\d = √((-2+3)^2+(-1+2)^2)\\\\d = √((1)^2+(1)^2)\\\\d = √(1+1)\\\\d = √(2)\\\\`

Coincidentally, the base and height are the same. This won't always be the case.

Now we can find the area of the triangle

`A = \text{Area of triangle}\\\\A = (1)/(2)*\text{Base}*\text{Height}\\\\A = (1)/(2)*√(2)*√(2)\\\\A = (1)/(2)*√(2*2)\\\\A = (1)/(2)*√(4)\\\\A = (1)/(2)*2\\\\A = 1\\\\`

The area of the triangle is 1 square unit.

See diagram below.