Plot each point and form the triangle ABC. Verify that the triangle is a right triangle. Find the area. A=(-5,3); B= ((6,0); C= (5,5) A=(4,-3); B=(4,1); C=(2,1)

Question

asked Feb 2, 2020 6.6k views

1 Answer

Dragut · Answer 1 · 2020-02-09T12:02:05+0000

Answer:

1) It is a right triangle.

$Area=25.93\ units^2$

2) It is a right triangle.

$Area=4\ units^2$

The points of each triangle are plotted in the images attached.

Explanation:

1) The points
A=(-5,3); B= ((6,0); C= (5,5) are plotted in the first image attached.

Knowing the points of the triangle, you can find the slope of
and
with this formula:

m=(y_2-y_1)/(x_2-x_1)

Then:

m_(AC)=(5-3)/(5-(-5))=(2)/(10)=(1)/(5)

m_(BC)=(5-0)/(5-6)=(5)/(-1)=-5

Since the slopes of the sides
and
are negative reciprocals, they are perpendicular; therefore IT IS A RIGHT TRIANGLE.

Find the length of
and
in order to calculate the area of the triangle:

$AC=√((-5-5)^2+(3-5)^2)=10.19\ units\\\\BC=√((5-6)^2+(5-0)^2)=5.09\ units$

The area is:

$A=(AC*BC)/(2)=((10.19\ units)(5.09\ units))/(2)=25.93\ units^2$

2) The points
A=(4,-3); B=(4,1); C=(2,1) are plotted in the second image attached.

By definition horizontal and vertical lines are perpendicular, therefore IT IS A RIGHT TRIANGLE.

You can observe in the figure that the lenghts of the sides
and
are:

$AB=4\ units$

$BC=2\ units$

Therefore, the area is:

$A=(AB*BC)/(2)=((4\ units)(2\ units))/(2)=4\ units^2$