The point which lies on the line y = -3x / 2 + 5 is
Answers
Step-by-step explanation:
Equation of the line is y = 2x
(a) Point A lies on the line y = 2x so it satisfies the equation of the line.
y=2(−2)=−4
Hence y coordinate of point A is -4.
(b) To verify whether a circle of radius 5 centred at point A(-2, -4) passes through the point B(5, 5) it is enough to show that the distance between point A and B is 5.
AB=
(5+2)
2
+(5+4)
2
=
49+81
=
130
=5
Hence a circle of radius 5 centred at point A(-2, -4) does not pass through the point B(5, 5).
(c) Let (x
1
,y
1
) be the coordinates of centre C on line.
Therefore it satisfies the equation of line a y = 2x
∴y
1
=2x
1
Also the distane between point B and C is radius that is 5.
So BC
2
=25
(x
1
−5)
2
+(y
1
−5)
2
=25
(x
1
−5)
2
+(2x
1
−5)
2
=25 [∵y
1
=2x
1
]
5x
1
2
−30x
1
+25=0
x
1
2
−6x
1
+5=0
(x
1
−5)(x
1
−1)=0
x
1
=5 or 1
y
1
=2x
1
=2(5)=10
y
1
=2x
1
=2(1)=2
The coordinates of point of C are (5, 10) or (1, 2).
Answer:
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