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the three lines y=2x y=6-x and y =-2 intersect to form a triangle PLEASE SHOW STEPS QUICK BEFORE BOTS

User GrzegorzM
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1 Answer

3 votes

Answer:

400 units^2

Explanation:

Its a bit much but.....

You have 3 lines that must intersect somewhere on those lines to form a triangle.

You know from the lines y = 23 and x = -6, that those two lines will intersect at point (-6, 23) and also form the opposite and adjacent legs of a right triangle.

The line y = 2x - 5 has a slope of 2 and a y-intercept of 5.

To find intersecting points, set two equations equal to each other (rearrange first) and solve for the unknown value:

y - 2x + 5 + 23 = y

-2x = -28

x = 14

So, the line y = 2x - 5 will intersect the line y = 23 at the point (14, 23)

Now to find where the line will intersect x = -6:

y = 2x - 5

0y = -2x - 12

y = -17

So, the line y = 2x + 5 will intersect the line x = -6 at point (-6, -17)

We know that the distance of a line is defined as x2 - x1 for horizontal lines.

We know that the distance of a line is defined as y2 - y1 for vertical lines.

So the distance of the x = -6 line is the y-values for the points were the line y = 2x + 5 intersects and where the line y = 23 intersects.

23 - (-17) = 23 + 17 = 40

The distance of the line x = -6 is 40 units.

14 - (-6) = 14 + 6 = 20

The distance of the line y = 23 is 20 units.

We know the area for a right triangle formula is A = ab/2:

A = 20(40)/2

A = 800/2

A = 400 units2

The area of the triangle formed by the the three lines is 400 units2

User Sake
by
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