Rectangle TUVW is on a coordinate plane at T(a,b) ,U(a+2,b+2),V(a+5,b-1) and W(a + 3, b - 3) )what is the slope of the line that is is parallel to the line that contains side WV?

Respuesta :

Answer:

The slope parallel to the line that contains side WV is 1.

Step-by-step explanation:

  1. The slope of parallel lines is also same.
  2. The product of perpendicular lines is -1.

Slope formula:

The slope of a line by joining two points (x₁,y₁) and (x₂,y₂) is

[tex]tan\theta=m= \frac{y_2-y_1}{x_2-x_1}[/tex]

Rectangle TUVW is on a coordinate plane at T(a,b), U(a+2,b+2),V(a+5,b-1) and W(a+3,b-3).

Here,x₁=a+3, y₁=b-3, x₂=a+5, y₂=b-1

Then the slope of line WV is

[tex]=\frac{(b-1)-(b-3)}{(a+5)-(a+3)}[/tex]

[tex]=\frac{b-1-b+3}{a+5-a-3}[/tex]

[tex]=\frac{2}{2}[/tex]

=1

Since the slope of parallel sides is always equal.

Then the slope parallel to the line that contains side WV is 1.

The slope of the line that is is parallel to the line that contains side WV is 1.

Given: In Rectangle TUVW

T(a, b), ,U(a+2,b+2),V(a+5,b-1) and W(a + 3, b - 3)

To find the slope of the line that is is parallel to the line that contains side WV.

The slopes of parallel lines are equal.

Let:

[tex](x_{1} , y_{1} )= W(a+3,b-3)\\(x_{2} , y_{2} )= W(a+5,b-1)[/tex]

The slope of a line by joining two points (x₁,y₁) and (x₂,y₂) is

[tex]m=\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Then the slope of line WV is

[tex]=\frac{(b-1)-(b-3)}{(a+5)-(a+3)} \\=\frac{b-1-b+3}{a+5-a-3} \\=\frac{2}{2} \\=1[/tex]

Therefore, The slope of the line that is is parallel to the line that contains side WV is 1.

For more information:

https://brainly.com/question/12203383

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