difference between the points (5, 1 ) (5, 5)
Answers
Answer:
Answer:-
Given:
Distance between the points (5 , - 2) ; (1 , a) is 5 units.
We know that,
Distance between two points \sf{(x_1 , y_1)}(x
1
,y
1
) and \sf{(x_2 , y_2)}(x
2
,y
2
) = \sf \large{\sqrt{{(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2}}}
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
\begin{gathered} \sf \implies \: \sqrt{ {(1 - 5)}^{2} + {(a + 2)}^{2} } = 5 \\ \end{gathered}
⟹
(1−5)
2
+(a+2)
2
=5
On squaring both sides we get,
\begin{gathered} \sf \implies{( \sqrt{ {( - 4)}^{2} + {(a + 2)}^{2} } })^{2} = {5}^{2} \\ \\ \sf \implies \: 16 + {(a + 2)}^{2} = 25 \\ \\ \sf \implies \: {(a + 2)}^{2} = 25 - 16 \\ \\ \sf \implies \: {(a + 2)}^{2} = 9 \\ \\ \sf \implies \: a + 2 = \sqrt{9} \\ \\ \sf \implies \: a + 2 = \pm 3 \\ \\ \implies \sf \large{ a = 1 \: (or) \: - 5}\end{gathered}
⟹(
(−4)
2
+(a+2)
2
)
2
=5
2
⟹16+(a+2)
2
=25
⟹(a+2)
2
=25−16
⟹(a+2)
2
=9
⟹a+2=
9
⟹a+2=±3
⟹a=1(or)−5
Hence, the value of a is 1 or - 5.
Answer:
(0,-4)
Step-by-step explanation:
5-5 0
1-5 -4