Given A(−1,2)
and B(3,6)
, find the coordinates of point X
on AB¯¯¯¯¯¯¯¯
such that the ratio of AX
to XB
is 3:5.(1 point)
Responses
(125,425)
Start Fraction 1 over 3 End Fraction
(112,112)
Start Fraction 2 over 1 End Fraction
(−14,312)
Start Fraction 3 over 2 End Fraction
(12,312)
Start Fraction 2 over 3 End Fraction
To find the coordinates of point X on the line AB such that the ratio of AX to XB is 3:5, we can use the section formula.
The section formula states that for a line segment AB with coordinates A(x1,y1) and B(x2,y2), the coordinates of a point X on AB such that AX:XB = m:n (where m and n are constants) can be found using the following formula:
X = (n * A + m * B) / (m + n)
In this case, A(-1,2) and B(3,6), and the ratio of AX to XB is 3:5.
So, substituting these values into the section formula:
X = (5 * (-1,2) + 3 * (3,6)) / (3 + 5)
= ( (-5,10) + (9,18) ) / 8
= (4,28) / 8
= (0.5, 3.5)
Therefore, the coordinates of point X are (0.5, 3.5).
None of the provided answer choices match this result.
where is the explanation bot
I apologize for the confusion. Here is the explanation:
To find the coordinates of point X on the line AB such that the ratio of AX to XB is 3:5, we can use the section formula.
The section formula states that for a line segment AB with coordinates A(x1,y1) and B(x2,y2), the coordinates of a point X on AB such that AX:XB = m:n (where m and n are constants) can be found using the following formula:
X = (n * A + m * B) / (m + n)
In this case, A(-1,2) and B(3,6), and the ratio of AX to XB is 3:5.
So, substituting these values into the section formula:
X = (5 * (-1,2) + 3 * (3,6)) / (3 + 5)
= ( (-5,10) + (9,18) ) / 8
= (4,28) / 8
= (0.5, 3.5)
Therefore, the coordinates of point X are (0.5, 3.5).
None of the provided answer choices match this result.
To find the coordinates of point X on the line segment AB, such that the ratio of AX to XB is 3:5, we can use the concept of section formula.
The section formula states that if you have two points A(x1, y1) and B(x2, y2), dividing the line segment AB in the ratio m:n will give you the coordinates of the point X as follows:
Coordinate of X = ((nx2 + mx1) / (m + n), (ny2 + my1) / (m + n))
In our case, we have A(-1, 2) and B(3, 6), with the ratio of AX to XB as 3:5.
Let's assign the values to the variables:
m = 3
n = 5
x1 = -1
x2 = 3
y1 = 2
y2 = 6
Now, substituting the values into the section formula, we get:
Coordinate of X = (((5 * 3) + (3 * -1)) / (3 + 5), ((5 * 6) + (3 * 2)) / (3 + 5))
Simplifying further, we have:
Coordinate of X = ((15 - 3) / 8, (30 + 6) / 8)
Coordinate of X = (12/8, 36/8)
Reducing the fractions, we have:
Coordinate of X = (3/2, 9/2)
Therefore, the coordinates of point X on AB, such that the ratio of AX to XB is 3:5, are (3/2, 9/2).