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Answer:
The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.
Step-by-step explanation:
Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. )
Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:
(3,5)-(1,1) and (0, 2)-(5, 12)
To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate. That will give us a valid Δx and Δy to get the slope.
In the first pair, 3 > 1, so we'll subtract the second point from the first:
So the first pair of vectors describe a line with a slope of 2. Let's look at the other pair:
That also gives us a slope of 2, meaning that the two lines are parallel.
This same process will need to be done for the other three questions. We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image. For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.
The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.
<h3>What is the line segment about?</h3>The law of the side- splitter connote that when f the line is parallel to a side of the triangle and if that said line do intersects the other 2 sides, tt is said to divides those given sides proportionally.
So the converse means that when the sides are proportional so therefore, the side TU is said to be parallel to the side RS.
Thus;
=
Therefore, the ratios are equal and as such TU is parallel to RS
Hence, The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.
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