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Byju's Answer
Standard IX
Mathematics
Distance Formula
If the point ...
Question
If the point P(k − 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k. [CBSE 2014]
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Solution
It is given that P(k − 1, 2) is equidistant from the points A(3, k) and B(k, 5).
∴ AP = BP
⇒
k
-
1
-
3
2
+
2
-
k
2
=
k
-
1
-
k
2
+
2
-
5
2
Distance
formula
⇒
k
-
4
2
+
2
-
k
2
=
-
1
2
+
-
3
2
Squaring on both sides, we get
k
2
-
8
k
+
16
+
4
-
4
k
+
k
2
=
10
⇒
2
k
2
-
12
k
+
10
=
0
⇒
k
2
-
6
k
+
5
=
0
⇒
k
-
1
k
-
5
=
0
⇒
k
-
1
=
0
or
k
-
5
=
0
⇒
k
=
1
or
k
=
5
Thus, the value of k is 1 or 5.
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If the point P(k − 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k. [CBSE 2014]
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