Prove that P(4,5) the point on AC and BD.

1.	Prove that P(4,5) the point on AC and BD.
Answer» AP = \(\sqrt{(4-2)^2+(5-3)^2}=2\sqrt{2}\) PC = \(\sqrt{(6-4)^2+(7-5)^2}=2\sqrt{2}\) AP + PC = 4√2 = AC ∴ P (4, 5) is a point on AC . BP = \(\sqrt{(4-5)^2+(5-4)^2}=\sqrt{2}\) PD = \(\sqrt{(3-4)^2+(6-5)^2}=\sqrt{2}\) BP + PD = √2 + √2 = 2√2 = BD ∴ P (4, 5) is also a point on BD.

Answer»

AP = \(\sqrt{(4-2)^2+(5-3)^2}=2\sqrt{2}\)

PC = \(\sqrt{(6-4)^2+(7-5)^2}=2\sqrt{2}\)

AP + PC = 4√2 = AC

∴ P (4, 5) is a point on AC .

BP = \(\sqrt{(4-5)^2+(5-4)^2}=\sqrt{2}\)

PD = \(\sqrt{(3-4)^2+(6-5)^2}=\sqrt{2}\)

BP + PD = √2 + √2 = 2√2 = BD

∴ P (4, 5) is also a point on BD.

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Prove that P(4,5) the point on AC and BD.

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