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two vertices of an obtuse triangle are $(6,4)$ and $(0,0)$. the third vertex is located on the negative branch of the $x$-axis. what are the coordinates of the third vertex if the area of the triangle is 30 square units?

Respuesta :

Lanuel

Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).

The types of triangle.

In Geometry, there are different types of triangle based on the length of their sides and angles, and these are;

  • Equilateral triangle
  • Scalene triangle
  • Isosceles triangle
  • Obtuse triangle
  • Right-angled triangle

How to calculate the area of a triangle?

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

  • b is the base area.
  • h is the height.

Note: The height of this triangle is the y-axis of (6, 4).

Substituting the given parameters into the formula, we have;

Area = 1/2 × b × h

30 = 1/2 × b × 4

2b = 30

b = 30/2

b = 15 units.

Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).

Read more on area of triangle here: https://brainly.com/question/20878930

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Complete Question:

Two vertices of an obtuse triangle are (6,4) and (0,0). The third vertex is located on the negative branch of the x-axis. What are the coordinates of the third vertex if the area of the triangle is 80 square units?

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