What is the area of triangle ABC?

Mathematics

1 answer:

miskamm [114]3 years ago

8 0

Answer:

<h2>7 square units</h2>

Step-by-step explanation:

As you can observe in the image attached, we know the coordinates of each vertex of the triangle.

To find the area using only its vertex coordinates, we need to use the following formula

$A=\frac{1}{2}[x_{1}(y_{2} -y_{3}+x_{2}(y_{3} -y_{1} )+x_{3}(y_{1}-y_{2} ) )$

Where the coordinates are

$A(1,1)\\B(4,0)\\C(3,5)$

Replacing coordinates, we have

$A=\frac{1}{2}[1(0 -5)+4(5 -1 )+3(1-0 ) ]\\A=\frac{1}{2} [-5+16+3]=\frac{1}{2}(14)\\ A=7$

Therefore, the area of the triangle is 7 square units. So, the right answer is the second choice.

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Use the image to match the arc/angle measure.

IrinaK [193]

Answer:

The following measurements are:

$m\angle{STR}=23^\circ$ (Option #4)

$m{QT}=142^\circ$ (Option #7)

$mST=134^\circ$ (Option #5)

$mRQ=38^\circ$ (Option #2)

Step-by-step explanation:

To begin, we can find the measure of $\angle{STR}$ by applying the inscribed angle theorem: an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

Since the intercepted arc (RS) is 46 degrees, we have:

$46=2\theta\\23=\theta$

Next, we can find the measure of arc QT using the same theorem. So,

$QT=2(71)\\QT=142$

Notice that the chord RT is actually a diameter. From the theorem about the inscribed angle including a diameter, we know that the intercepted arc will have a measure of $180^\circ$ . Since the arc ST is part of the arc RST, and we know RS is $46^\circ$ , we can set up and solve this equation: