Question

Find the coordinate of point y on AC that is 1/4 of the distance from a to c

Answer 1

The coordinates of point C, denoted as
`\(x_C\)`, can be either 3 or 13. This is determined by the condition that the distance between points B and C is one-fourth of AB.

Let's denote the coordinates of points A, B, and C as
`\(x_A\), \(x_B\), and \(x_C\)` respectively.

Given that the distance between points B and C is one-fourth of AB, we can set up the following equation:

`\[BC = (1)/(4)AB\]`

The distance between two points is given by the absolute difference of their coordinates. Therefore:

`\[|x_B - x_C| = (1)/(4)|x_A - x_B|\]`

Given that the coordinates of points A and B are
`\(x_A = -12\) and \(x_B = 8\)`, we can substitute these values into the equation:

`\[|8 - x_C| = (1)/(4)|(-12) - 8|\]`

Simplify the equation:

`\[|8 - x_C| = (1)/(4)|-20|\]`

`\[|8 - x_C| = 5\]`

Now, solve for
`\(x_C\)` by considering both positive and negative cases:

Case 1:
`8 - x_C = 5`

`\[x_C = 8 - 5 = 3\]`

Case 2:
`\(x_C - 8 = 5\)`

`\[x_C = 8 + 5 = 13\]`

Therefore, the coordinates of point C are
`\(x_C = 3\)` or
`\(x_C = 13\).`

Que. Point C is between points A and B. The distance between points B and C is 1/4 of AB. What is the coordinate of point C?