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Vaselesa [24]
2 years ago
5

On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 1), point B is at (3, 2), and points C is at (negativ

e 1, negative 1) If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle? 0. 625 units 0. 8 units 1. 25 units 1. 6 units.
Mathematics
1 answer:
oksian1 [2.3K]2 years ago
8 0

The corresponding height of the triangle is 1.6 units

The formula for calculating the area of a triangle is expressed as:

A=\frac{1}{2} bh

  • b is the base of the triangle
  • h is the height of the triangle

Given the coordinates of the base BC of the triangle given as B(3, 2), and C(-1,-1). Using the distance formula:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\BC= \sqrt{(-1-2)^2+(-1-3)^2}\\BC=\sqrt{3^2+4^2}\\BC=\sqrt{25}\\BC=5units

The area of the triangle passing through the coordinate points A(-1, 1), B(3,2), and C(-1, -1) is expressed as:

A=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]\\

Substituting the coordinate points:

A=\frac{1}{2}[(-1)(2-(-1))+3(-1-1)+-1(1-2)]\\A=\frac{1}{2}[(-1)(3)+3(-2)+-1(-1)]\\A=\frac{1}{2}[-3-6+1]\\A=\frac{1}{2} (-8)\\|A| =4 units^2

Recall that:

A = 0.5bh\\h=\frac{A}{0.5b}\\h=\frac{4}{0.5(5)}\\h=\frac{4}{2.5}\\h=   1.6 units

Hence the corresponding height of the triangle is 1.6 units

Learn more on area of triangles here: brainly.com/question/17335144

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