This week laptops are 25% off. If a laptop cost $340 what is it's sale price?
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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.
Since the triangles are similar, the ratio of the sides of larger triangle to the smaller triangle is a constant.
That constant =
Since the sides are in that constant proportion, the area of the triangles will also be in proportion.
(Area of larger triangle) over (Area of smaller triangle) =
= 123.6 ≈ 124
Hence, to the nearest whole number the area of smaller triangle is 124 <span>ft</span>²<span>.</span>
That constant =
Since the sides are in that constant proportion, the area of the triangles will also be in proportion.
(Area of larger triangle) over (Area of smaller triangle) =
Hence, to the nearest whole number the area of smaller triangle is 124 <span>ft</span>²<span>.</span>