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anzhelika [568]
3 years ago
9

What is (2,7) rotated 90% clockwise

Mathematics
1 answer:
ohaa [14]3 years ago
5 0

Answer:

The required point is, (7, -2)

Step-by-step explanation:

The straight  line passing through (0,0) and (2,7) is,

y = (\frac {7 -0}{2-0}) \times x

⇒ y = 3.5x --------------(1)

Now, the straight line perpendicular to this line and passing through (0, 0) is

y = (\frac {-1}{3.5}) \times x

⇒ 7y + 2x = 0 -------------(2)

Let, (h,k) be the required point.

then, it is on the line 7y + 2x = 0

⇒7k + 2h = 0

⇒k = (\frac {-2}{7}) \times h ------------(3)

Again, distance from (0,0) of (h, k) is same as that of (2,7)

⇒ h^{2} + k^{2} = 4 + 49 = 53

⇒h^{2} \times (\frac {53}{49}) = 53 [putting the value of k from (3)]

⇒h^{2} = 49

⇒h = 7 [since, (h,k) is in 4th quadrant, so,h >0]

So, k = -2 [putting the value of h in (3)]

So, the required point is, (7, -2)

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