Question
Download Solution PDFIf the distances of P (x, y) from A (4, 1) and B (-1, 4) are equal, then which of the following is true?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The distance 'd' between two points (x1, y1) and (x2, y2) is obtained by using the Pythagoras' Theorem: d2 = (x1 - x2)2 + (y1 - y2)2.
Calculation:
Using the formula for the distance between two points:
AP2 = (x - 4)2 + (y - 1)2
BP2 = (x + 1)2 + (y - 4)2
Since the distances are equal, we have:
AP2 = BP2
⇒ (x - 4)2 + (y - 1)2 = (x + 1)2 + (y - 4)2
⇒ x2 - 8x + 16 + y2 - 2y + 1 = x2 + 2x + 1 + y2 - 8y + 16
⇒ 10x = 6y
⇒ 5x = 3y.
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