Graph each set of lines to form a triangle, then find the area and perimeter.

Question

Y=-5, x=2, and y=-2x+7

Answer 1

The sides of the triangle are y = - 5, x = 2, y = - 2x + 7

1). Draw a coordinate plane.

2). Draw the  horizontal line y = - 5 and vertical line x = 2.

3). The line is y = - 2x + 7.

Compare the equation with slope-intercept form y = mx + b, where, m is slope and b is y - intercept.

slope = - 2 and y-intercept is 7.

y-intercept is 7, so the line crosses the y-axis at (0, 7)

Using slope find the next point.

Slope = rise/run = - 2/1

Start at point (0, 7), move 2 units down and 1 unit right, then plot the point (1, 5).

Draw a line through these points.

GRAPH :

Answer 2

4).From the graph,

The lines y = - 5, x = 2, and y = - 2x + 7 form a triangle ABC.

The lines x = 2 and y = - 2x + 7 are intersect a point A(2, 3).

The lines y = - 5 and x = 2 are intersect at a point B(2, - 5), and

The lines y = - 5 and y = - 2x + 7 are intersect at a point C(6, - 5).

5). To find AB, BC, and AC use distance formula.

Note : if A = (x₁, y₁) and B = (x₂, y₂) then the distance between A and B is √[ (x₂ - x₁)^2 + (y₂ - y₁)^2 ].

6). AB = √[ (2 - 2)^2 + (- 5 - 3)^2 ]

     = √[ 0 + (- 8)^2 ]

     = √64

     = 8.

BC = √[ (6 - 2)^2 + (- 5 + 5)^2 ]

     = √[ (4)^2 + 0 ]

     = 4.

AC = √[ (6 - 2)^2 + (- 5 - 3)^2 ]

     = √[ (4)^2 + (- 8)^2 ]

     = √[ 16 + 64 ]

    = √80 = 4√5.

7). From pythagorean theorem,

AC^2 = AB^2 + BC^2

(√80)^2 = 8^2 + 4^2

→ 80 = 64 + 16 = 80.

The abov estatement is true, so, triangle ABC is a right triangle.

8). Perimeter of the triangle ABC = AB + BC + AC

                                         = 8 + 4 + 4√5

                                         = 12 + 4√5

                                         = 4(3 + √5) units.

9). Area of the triangle ABC = 1/2 * BC * AB

                                    = 1/2 * 4 * 8

                                    = 16 square units.