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Lines MN and PQ are parallel. Lines RS and TV intersect them.

On a coordinate plane, 3 lines are shown. Line M N has points (negative 3, negative 1) and (3, 3). Line P Q has points (negative 3, negative 4) and (3, 0.5). Line R S has points (negative 2, 4) and (2, negative 2).
Which statements are true about these lines? Select three options.

The slope of line MN is Two-thirds.
The slope of line PQ is undefined.
The slope of line RS is Negative three-halves.
Lines RS and TV are parallel.
Line RS is perpendicular to both line MN and line PQ



Answer :

Answer:

1. The slope of line MN is Two-thirds.

2. Lines RS and TV are parallel.

3. Line RS is perpendicular to both line MN and line PQ.

Step-by-step explanation:

The true statements about these lines are:

1. To find the slope of line MN, we use the formula: slope = (change in y) / (change in x). So, slope of MN = (3 - (-1)) / (3 - (-3)) = 4 / 6 = 2/3.

2. Lines RS and TV are parallel because they have the same slope. The slope of RS is: slope = (-2 - 4) / (2 - (-2)) = -6 / 4 = -3/2.

3. For a line to be perpendicular to another, their slopes are negative reciprocals of each other. The slope of RS is -3/2, and the slope of both MN and PQ is 2/3, the negative reciprocal of -3/2. Therefore, RS is perpendicular to both MN and PQ.

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