In ΔNOP, the measure of ∠P=90°, NP = 45, ON = 53, and PO = 28. What ratio represents the secant of ∠N?
2 answers:
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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
