Question

1.The following are conditions that tells us that lines or segment are parallel EXCEPT.
a.corresponding angles are equal
b.alternate interior angles are equal
c.slopes are negative reciprocal of one another
d.lines or segment do not intersect no matter how they extended
2.The following are conditions that tells us that lines or segment are perpendicular EXCEPT.
a.slopes formed by the lines are equal
b.angles formed by the lines measures 90°
c.slopes are negative reciprocal of one another
d.lines or segments are intersected at a common point
For no.3-5 LINE 1:A(-2,4) B(2,2) LINE 2:C(4,-8) D(-8,-2)
3.the slope line 1 is.
a-2 c.1/2
b.-1/2(one half) d.2
4.the slope line 2 is.
a.-2 c.1/2
b.-1/2 d.2
5.the lines are?
a.Parellel lines c.Neither parallel nor perpendicular
b.Perpendicular lines d.None of these

Answer 1

Answer:

1. c.slopes are negative reciprocal of one another

2. a.slopes formed by the lines are equal

3. b.-1/2

4.b.-1/2

5. Parellel lines

hope the answer helps

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Answer 2

Concept

• Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Parallel lines' slopes are equal.

• The definition of a perpendicular line in geometry is a pair of lines that meet or intersect at right angles (90°). Perpendicular line slopes are the negative reciprocals of one another.

• We know that a straight line passing through the points (x₁, y₁) and (x₂, y₂) can be written as

y - y₁ = (y₂ - y₁)(x - x₁)/(x₂ - x₁)

Given

1. Given that two lines are parallel.

2. Given that two lines are perpendicular.

3. Given that line 1 passes through points A(- 2, 4) and B(2, 2).

4. Given that line 2 passes through points C(4, - 8) and D(- 8, - 2).

5. Requirements of line 1 and 2 are given.

Find

We have to find

1. which statement is true for parallel lines.

2. which statement is true for perpendicular lines.

3. the slope of line 1.

4. the slope of line 2.

5. which option is true for line 1 and line 2.

Solution

1. From the definition of parallel lines, we can say that the slopes of two parallel lines or segments are not negative reciprocals of one another. So, option c is correct.

2. From the definition of perpendicular lines, we can say that the slopes of two perpendicular lines or segments not formed by the lines are equal. So, option a is correct.

3. Here, x₁ = - 2, y₁ = 4, x₂ = 2 and y₂ = 2.

The equation of line 1 is

y - 4 = (2 - 4)(x - (- 2))/(2 - (- 2)) = (- 2)(x + 2)/(2 + 2) = (- 2)(x + 2)/4 = (- ½)(x + 2)

i.e. y - 4 = (- ½)(x + 2)

i.e. y = (- ½)x + (- ½) * 2 + 4

i.e. y = (- ½)x - 1 + 4

i.e. y = (- ½)x + 3

Slope of line 1 = co-efficient of x = (- ½)

So, option b is correct.

4. Here, x₁ = 4, y₁ = - 8, x₂ = - 8 and y₂ = - 2.

The equation of line 2 is

y - (- 8) = ( - 2 - (- 8))(x - 4)/(- 8 - 4) = (- 2 + 8)(x - 4)/(- 12) = 6(x - 4)/(- 12) = (- ½)(x - 4)

i.e. y + 8 = (- ½)(x - 4)

i.e. y = (- ½)x - (- ½) * 4 - 8

i.e. y = (- ½)x + 2 - 8

i.e. y = (- ½)x - 6

Slope of line 2 = co-efficient of x = (- ½)

So, option b is correct.

5. Since the slope of line 1 = the slope of line 2 = (- ½)

We can conclude that the lines are parallel. So, option a is correct.

Therefore,

1. The following are conditions that tell us that lines or segments are parallel EXCEPT slopes are negative reciprocals of one another. So, option c is correct.

2. The following are conditions that tell us that lines or segments are perpendicular EXCEPT slopes formed by the lines are equal. So, option a is correct.

3. The slope of line 1 is (- ½). So, option b is correct.

4. The slope of line 2 is (- ½). So, option b is correct.

5. Lines 1 and 2 are parallel lines. So, option a is correct.

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