If A(4,2) B(1, y) and AB=5 then y=
a)6 and -2
b) -6 and 2
c) +/-6
d) +/-2
Please show the process
Related to Coordinate Geometry
Answers
Answered by
0
Step-by-step explanation:
Distance formula between to points A(x
1
,y
1
) and B(x
2
,y
2
) is equal to
AB=
(y
2
−y
1
)
2
+(x
2
−x
1
)
2
According to the given condition,
5=
(y−2)
2
+(1−y)
2
⇒25=y
2
+4+y
2
+1−4y−2y
⇒2y
2
−6y−20=0
⇒y
2
−3y−10=0
⇒y
2
−5y+2y−10=0
⇒y(y−5)+2(y−5)=0
⇒y=5,−2
Answered by
1
Answer:
y will be equal to +/-6
Step-by-step explanation:
Given,
A = (4,2), B = (1,y), AB = 5
using the distance formula
AB = [ (x2 - x1)^2 - (y2 - y1)^2 ]^1/2
substitute the values
5 = [ (1 - 4)^2 + (y - 2)^2 ]^1/2
5 = [ (-3)^2 + (y - 2)^2]^1/2
(5)^2 = 9 + (y - 2)^2
25 -9 = ( y - 2)^2
16 = ( y - 2)^2
(16)^1/2 = y - 2
4 = y - 2
y = 6
Therefore, y = +/-6
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