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62. Triangle ABC has vertices as shown.
What is the area of the triangle?
A. √72 square units
B. 12 square units
C. √288 square units
D. 24 square units

A(1,4)
B(4,1)
C(-3,0)

62 Triangle ABC has vertices as shown What is the area of the triangle A 72 square units B 12 square units C 288 square units D 24 square units A14 B41 C30 class=

Respuesta :

mhanifa

Answer:

  • B. 12 square units

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We can see AB and AC are perpendicular.

Verify it by comparing slopes:

  • Slope of AB = (1 - 4)/(4 - 1) = - 3/3 = - 1
  • Slope of AC = (0 - 4)/(- 3 - 1) = - 4/ - 4 = 1

Since the product of the slopes is - 1, the segments are perpendicular.

Find the length of AB and AC:

  • [tex]AB=\sqrt{(4-1)^2+(1-4)^2}=\sqrt{9+9} =\sqrt{9*2} =3\sqrt{2}[/tex]
  • [tex]AC=\sqrt{(1+3)^2+(0-4)^2}=\sqrt{16+16} =\sqrt{16*2} =4\sqrt{2}[/tex]

Find the area:

  • [tex]A = 1/2*AB*AC=1/2*3\sqrt{2}*4\sqrt{2}=12[/tex]

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