The mid-point of the line segment joining (3, 6) and
(x, 2) is (2, y). Find the values of x and y.
Answers
Answer:
X(a,2),Y(3,6),Z(2,b)
Z=(
2
x
1
+x
2
,
2
y
1
+y
2
)
(2,b)=(
2
a+3
,
2
2+6
)
(2,b)=(
2
a+3
,4)
2=
2
a+3
,b=4
4=a+3,b=4
a=1,b=4
Explanation:
Answer:
The value of a is 1 and the value of b is 4 .
Step-by-step explanation:
Formula for midpoints
(x , y) = (\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2})(x,y)=(
2
x
1
+x
2
,
2
y
1
+y
2
)
Where (x ,y ) are the midpoints .
As given
The midpoint of the line segment joining the points ( a, 2) and ( 3, 6) is (2, b) .
x = 2
x_{1}=ax
1
=a
x_{2}=3x
2
=3
y = b
y_{1}=2y
1
=2
y_{2}=6y
2
=6
Put all the values in the formula
(2 , b) = (\frac{a+3}{2} , \frac{2+6}{2})(2,b)=(
2
a+3
,
2
2+6
)
Now compare the terms
2 = \frac{a + 3}{2}2=
2
a+3
2 × 2 = a + 3
4 = a + 3
a = 4 - 3
a = 1
b =\frac{2+6}{2}b=
2
2+6
b = \frac{8}{2}b=
2
8
b = 4
Therefore the value of a is 1 and the value of b is 4 .