If a line (-9,7) is marked by e which is a ratio of 1/4 then where is e on the line?
My answer is -7
To find the point on the line represented by the ratio 1/4, you can use the formula:
P = A + r(B - A)
where P is the desired point, A is one point on the line, B is another point on the line, and r is the ratio.
In this case, the point A is given as (-9,7). To find point B, we need to use the given ratio of 1/4. This means that the line segment between A and B is divided into four equal parts, with e representing the first part. Therefore, the ratio r for point e is 1/4.
Next, we need to find B. Since we know that the line segment is divided into four equal parts, we can find B by finding the four times the difference between A and B:
B = A + 4(B - A)
Simplifying the equation, we get:
B = 4A - 3B
Rearranging the equation to solve for B, we have:
4B = 4A + 3B
Combining like terms, we get:
B = 7A
Substituting the value of A as (-9,7), we have:
B = 7(-9,7) = (-63, 49)
Now, we can find the point e by plugging in the values of A, B, and the ratio r into the formula:
e = A + r(B - A)
e = (-9,7) + (1/4)((-63, 49) - (-9,7))
Simplifying the equation, we have:
e = (-9,7) + (1/4)(-54, 42)
e = (-9,7) + (-13.5, 10.5)
Adding the coordinates, we get:
e = (-9 - 13.5, 7 + 10.5)
e = (-22.5, 17.5)
Therefore, the point e on the line is (-22.5, 17.5), not -7 as you previously suggested.