the mid point of the line segment joining (4a, 2b-3) and (-4,3b) is (2,2a) find the values of 'a'and 'b'.
To find the midpoint of a line segment, we can use the formula:
Midpoint = ((x1+x2)/2, (y1+y2)/2)
From the given information, we know that the midpoint is (2,2a) and the two points on the line segment are (4a, 2b-3) and (-4, 3b). So we can set up our equation as:
(4a + (-4))/2 = 2
2a + 0 = 2
2a = 2
a = 1
Now let's find the value of b. We know that the y-coordinate of the midpoint is 2a, so:
(2b-3 + 3b)/2 = 2a
(5b-3)/2 = 2a
5b-3 = 4a
5b-3 = 4(1)
5b-3 = 4
5b = 4+3
5b = 7
b = 7/5
So, the values of a and b are a = 1 and b = 7/5.
To find the values of 'a' and 'b' from the given information, we can use the midpoint formula.
The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
According to the problem, the midpoint of the line segment joining (4a, 2b-3) and (-4,3b) is (2,2a).
Therefore, we can equate the x-coordinate and y-coordinate separately and solve for 'a' and 'b'.
Equating the x-coordinate:
((4a + (-4))/2) = 2
Simplifying:
(4a - 4)/2 = 2
4a - 4 = 2 * 2
4a - 4 = 4
4a = 4 + 4
4a = 8
a = 8/4
a = 2
Equating the y-coordinate:
((2b - 3 + 3b)/2) = 2
Simplifying:
(5b - 3)/2 = 2
5b - 3 = 2 * 2
5b - 3 = 4
5b = 4 + 3
5b = 7
b = 7/5
Therefore, the values of 'a' and 'b' are a = 2 and b = 7/5.
To find the values of 'a' and 'b', we can use the midpoint formula. The formula for finding the midpoint between two points is:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that the midpoint is (2, 2a), we can set up the equation as follows:
2 = (4a - 4) / 2
2a = (2b - 3 + 3b) / 2
Simplifying the first equation:
2 = 2a - 2
4 = 2a
a = 2
Substituting the value of 'a' back into the second equation:
2(2) = 2b - 3 + 3b
4 = 5b - 3
7 = 5b
b = 7/5
Therefore, the values of 'a' and 'b' are 2 and 7/5, respectively.