Question

Line WV is perpendicular to both line RS and line TU. On a coordinate plane, 3 lines are shown. Line V W goes through (negative 1, 5) and (1, 5). Line R S goes through (negative 5, 3) and (5, 1). Line T U goes through (negative 1, negative 2) and (4, negative 3). Which statement must be true about line TU? Line TU is parallel to line RS. Line TU is perpendicular to line RS. Line TU has no slope. Line TU has a slope of –5.

Answer 1

A

Step-by-step explanation:

Answer 2

The True statement for a line TU is

Line TU is parallel to line RS

Step-by-step explanation:

Given:

Let,

point R( x₁ , y₁) ≡ ( -5, 3)

point S( x₂ , y₂) ≡ (5 , 1)

and

point T( x₁ , y₁) ≡ ( -1, -2)

point U( x₂ , y₂) ≡ (4 , -3)

We have Line RS and Line TU

Slope of any Line having Two points ( x₁ , y₁) and ( x₂ , y₂) Given by

`Slope=(y_(2)-y_(1) )/(x_(2)-x_(1) )`

`\therefore Slope(RS)=(y_(2)-y_(1) )/(x_(2)-x_(1) )\\\\\\\\\therefore Slope(RS) =(1-3)/(5-(-5) )\\\\\therefore Slope(RS) =(-2)/(10)\\\\\therefore Slope(RS) =(-1)/(5)\\`

Similarly,

`\therefore Slope(TU)=(y_(2)-y_(1) )/(x_(2)-x_(1) )\\\\\\\\\therefore Slope(TU) =(-3-(-2))/(4-(-1) )\\\\\therefore Slope(TU) =(-1)/(5)\\\\\therefore Slope(RS) =(-1)/(5)\\`

Now,

Slope of RS = Slope of TU

We Know, if the slopes are equal then the lines are parallel.

Therefore line TU is parallel to line RS is the true statement about line TU.