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pishuonlain [190]
4 years ago
8

Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*

Mathematics
1 answer:
Veronika [31]4 years ago
4 0

Answer:

<em>The area of the triangle DEF is 10.</em>

Step-by-step explanation:

<u>Area of a Triangle:</u>

A triangle of base B and height H (both must be perpendicular) has an area of:

\displaystyle A=\frac{BH}{2}

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

\displaystyle A=\frac{5*4}{2}=10

The area of the triangle DEF is 10.

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Write the equation of the line that passes through the given point and is parallel to the given line.
romanna [79]

<u>(Note: this answer is assuming that the equation has to be put in slope-intercept format.)</u>

Answer:

y = \frac{1}{2} x - \frac{5}{2}

Step-by-step explanation:

1) Let's use the point-slope formula to determine what the answer would be. To do that though, we would need two things: the slope and a point that the equation would cross through. We already have the point it would cross through, (-3,-4), based on the given information. So, in the next step, let's find the slope.

2) We know that the slope has to be parallel to the given line, y = \frac{1}{2}x - 8. Remember that slopes that are parallel have the same slope - so, let's simply take the slope from the given equation. Since it's already in slope-intercept form, we know that the slope then must be \frac{1}{2}.

3) Finally, let's put the slope we found and the x and y values from (-3, -4) into the point-slope formula and solve:

(y- (-4))  = \frac{1}{2} (x - (-3))\\y + 4 = \frac{1}{2} (x + 3))\\y + 4 = \frac{1}{2}x+ \frac{3}{2} \\y = \frac{1}{2}x + \frac{3}{2} - 4\\y =  \frac{1}{2}x + \frac{3}{2} - \frac{8}{2} \\y = \frac{1}{2}x - \frac{5}{2}

Therefore, y = \frac{1}{2}x - \frac{5}{2} is our answer. If you have any questions, please do not hesitate to ask!

3 0
3 years ago
Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the trian
Pachacha [2.7K]

Answer:

m=1/300 du

Step-by-step explanation:

we have that m=∫∫rho(x,y)dA for this we must find the limits of integration (according to the graph1)

On the x axis: if y=2x and x+2y=1 then y=2x and y=(1-x)/2 ⇒ 2x=(1-x)/2 ⇒ 4x=1-x ⇒ 5x=1 ⇒ x=1/5; on the y axis y=0 and y=1/2

m=∫∫rho(x,y)dA (view the graph 2)

4 0
3 years ago
Plz answer for a brainly, ill give u brainliy and 100 points
bezimeni [28]

Answer:

what is this

Step-by-step explanation:

what's the question

5 0
3 years ago
Read 2 more answers
Enter the value of <br><br> 3 + (10 x 12) – 7
Margarita [4]

Answer:

116

Step-by-step explanation:

Pemdas so do the 10 × 12 first... you get 120 the you go left to right so 3 + 120 = 123... subtract 7 from that and you get 116.

7 0
2 years ago
I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT!!!
GrogVix [38]
It is g(x) =2 there I guessed hope correct.
8 0
3 years ago
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