Question

if the points P (K - 1, 2) is equal distance from the point A (3 ,k) and B (K, 5) find the value of k​

Answer 1

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Answer

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Value of k will 1 or 5

Given

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↗Coordinate of P(k-1 , 2) Coordinate of A(3 ,k) and coordinate of B(k,5)

↗AP = BP

Solution

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Firstly we have to find out the value of AP

x1 = K-1 x2 = 3

y1 = 2. y2 = k

distance formula

$\sqrt{(x2 - x1) +( y2 - y1)}$

Applying distance formula

$ap = \sqrt{ {(3 - (k - 1)}^{2} ( {k - 2)}^{2} }$

$ap = \sqrt{ {(4 - k)}^{2} + {k}^{2} + 4 - 4k }$

$ap = \sqrt{16 + {k}^{2} - 8k + {k}^{2} + 4 - 4k }$

$ap = \sqrt{2 {k}^{2} - 12k + 20 }$

Now we have to find out the value of BP

$bp = \sqrt{( {k - k + 1)}^{2} + {(3)}^{2} }$

$bp = \sqrt{1 + 9}$

$bp = \sqrt{10}$

As given

AP = BP

Squaring both sides.

AP² = BP²

${ap}^{2} = 2 {k}^{2} - 12k + 20$

${bp}^{2} = 10$

Calculation

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Putting both equations equal

2k² - 12k + 20 = 10

Taking 2 common both sides.

k² - 6k + 10 =. 5

k² - 6k + 10 - 5 = 0

k² - 6k +5 =0

Now splitting mid term

k² -k - 5k +5 = 0

k(k -1) -5 (k- 1) °= 0

(k -1) (k- 5) = 0

K = 1

or

K = 5

hope it helps

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