Question
the mid point of the line segment joining (4a, 2b-3) and (-4,3b) is (2,2a) find the values of 'a'and 'b'.
Answers
GPT 3.5
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.
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.