COORDINATE GEOMETRY
CLASS 10
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•Please answer the question in the picture.
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THANKS...
Answers
Solution :
If P(2,4) is equidistant from Q(7,0) & R(x,9).
The value of x & the distance of PR .
We know that formula of the distance;
A/q
PQ = PR
&
Squaring both the side;
Now;
Thus;
The distance of PR will be √41 .
Given:
P(2, 4)
Q(7, 0)
R(x, 9)
P is equidistant from Q & R.
In simple words, PQ = PR
To Find:
Value of x.
Distance of PQ.
Solution:
ATQ:
Squaring on both sides we get:
Applying Distance Formula we get:
For PQ:
x₁ = 2
x₂ = 7
y₁ = 4
y₂ = 0
For PR
x₁ = 2
x₂ = x
y₁ = 4
y₂ = 9
Squares and roots get cancelled.
Using (a - b)² = a² + b² - 2ab we get:
∴ x = 6 or x = - 2.
But, one of the values might not be the correct value, so let's cross-check with this equation that we've got from one of the steps of the previous part:
Case I
When x = 6
Therefore x = 6 is correct.
Case II
When x = -2
Therefore x = -2 is also correct.
Hence, the values of x are 6 & -2.
Now, we have to find the distance of PQ.
Using the Distance Formula we get:
Final answers:
⇔ The values of x are 6 and -2.
⇔ The distance of PQ is sq.units.