Simplify:(2 + i) - (-3+9i)
1 answer:
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Answer:
shown in explanation
Step-by-step explanation:
a) ∆EPB similar to ∆ERG
b) angle BEP = angle GER (common angle shared)
angle EPB = angle ERG (corresponding angles, PB//RG, parallelogram)
therefore through Angle-Angle similarity test, ∆EPB is similar to ∆ERG
or explanation can also be shortened to
∆EPB is similar to ∆ERG (AA, similarity)
c) since proven they are similar ∆, then we can proceed to use property of ratio of corresponding sides being equal
RG = 200+300=500m
cross multiply (from what I've learnt)
2ep+700=5ep
ep= 700/3 = 233 ⅓m (answer for length EP)
Do the same for length BE(using ratio of corresponding sides)
cross multiply again to get:
5BE = 2BE + 800
BE = 800/3 = 266 ⅔ m (answer for length BE)
Answer:
(-8, 3), (8, -3)
Step-by-step explanation:
Point symmetry about origin means reflection of the given point about the origin.
The reflection of a point about the origin will cause the 'x' and 'y' value of the point to change its sign.
Therefore, the coordinate rule for point symmetry about the origin is given as:
Now, let us check each of the given options.
Option 1:
(-8, 3), (8, -3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3)
So, option 1 is correct.
Option 2:
(-8, 3), (-3, 8)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-3, 8)
So, option 2 is not correct.
Option 3:
(-8, 3), (-8, -3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-8, -3)
So, option 3 is not correct.
Option 4:
(-8, 3), (8, 3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (8, 3)
So, option 4 is not correct.
Hence, only option 1 is correct.