Answer:
1 and 2.
Midpoints calculated, plotted and connected to make the triangle DEF, see the attached.
- D= (-2, 2), E = (-1, -2), F = (-4, -1)
3.
As per definition, midsegment is parallel to a side.
Parallel lines have same slope.
<u>Find slopes of FD and CB and compare. </u>
- m(FD) = (2 - (-1))/(-2 -(-4)) = 3/2
- m(CB) = (1 - (-5))/(1 - (-3)) = 6/4 = 3/2
- As we see the slopes are same
<u>Find the slopes of FE and AB and compare.</u>
- m(FE) = (-2 - (- 1))/(-1 - (-4)) = -1/3
- m(AB) = (1 - 3)/(1 - (-5)) = -2/6 = -1/3
- Slopes are same
<u>Find the slopes of DE and AC and compare.</u>
- m(DE) = (-2 - 2)/(-1 - (-2)) = -4/1 = -4
- m(AC) = (-5 - 3)/(-3 - (-5)) = -8/2 = -4
- Slopes are same
4.
As per definition, midsegment is half the parallel side.
<u>We'll show that FD = 1/2CB</u>
- FD =
= 
= 
- CB =
= 
= 2 - As we see FD = 1/2CB
<u>FE = 1/2AB</u>
- FE =
= 
= 
- AB =
= 
= 2 - As we see FE = 1/2AB
<u>DE = 1/2AC</u>
- DE =
= 
= 
- AC =
= 
= 2 - As we see DE = 1/2AC
Answer: Choice B
{(0,0), (1,2), (2,4), (3,4)}
===============================================
Explanation:
A function is only possible if each x input leads to exactly one y output. For choice A, we have x = 1 lead to y = 3 and y = 5 at the same time, which is what the points (1,3) and (1,5) are saying. Therefore, choice A is not a function.
Choice C is also ruled out because x = 2 repeats itself as well. In this case, (2,3) and (2,4) means that the input x = 2 leads to the two outputs y = 3 and y = 4.
Choice D can be eliminated also for two reasons: x = 0 shows up twice, so does x = 2.
Only choice B has each x value listed one time only. So that means each input leads to exactly one output.
If you graph choice A, C or D, you'll find they fail the vertical line test. The vertical line test is where you test if you can draw a vertical line through more than one point on the graph. If you can draw a vertical line through more than one point on the graph, then the relation fails to be a function.
Let Brian's steps have a measure of 1, and Richard's steps have a measure of k. Then after each walks 5 steps away from the other, their distance apart is
... 5 + 5k
We are told that distance is equal to 9 of Richard's steps, so is equal to 9k.
... 5 + 5k = 9k
... 5 = 4k . . . . . . . subtract 5k
... 5/4 = k . . . . . . divide by 4
Richard's steps are 5/4 the size of Brian's steps. The appropriate selection is
... b) 5/4
