Question

What is the area of a triangle with vertices at (-4,1),(-7,5),and (0,1)

Answer 1

Answer:Find out the magnitude of each line segment

A=(-4, 1)

B= (-7, 5)

C=(0, 1)

Plot out the triangle to find out what the general shape of the triangle looks like since we need height.

A-B= √(-4+7)²+(1-5)²

=5

B-C=√(-7)²+(5-1)²

= √53

C-A=√(4)²+(1-1)²

=4

Find midpoint of B-C because line segment between A and B-C would be the height (according to the rough sketch previously drawn)

B-C= (x, y)= (x₁+x₂/2), (y₁-y₂/2)

(x, y)= (-7+0/2), (5+1/2)

(x, y)= -3.5, 3

Magnitude of A-BC:

√(-3.5+4)²(3-1)²

=√(0.5)²+4

Area=1/2(bh)

a=1/2(√53)(√(0.5)²+4 )

a= 7.5

Hope I helped you understand how you can derive the answer yourself :)

Step-by-step explanation: