The graphs of 𝑓(𝑥) =− 2𝑥 and are drawn (not to 2 − 4𝑥 + 30 𝑔(𝑥) = 2𝑥 + 10

Let's analyze the functions given in your problem and find the points mentioned based on their properties.

### Functions:
- \( f(x) = -2x \)
- \( g(x) = 2x + 10 \)

### 6.1 Determine the coordinates of \( A, B, C, \) and \( D \).

1. **X-intercepts (A and B) of \( f(x) \)**: To find the x-intercepts, set \( f(x) = 0 \):
\[
-2x = 0 \implies x = 0
\]
So, \( A \) at \( (0, 0) \).

2. We aren't given the limits of \( A \) and \( B \) explicitly in the problem. With \( f(x) = -2x \) indicating a straight line declining through the origin, if we assume the graph shows a positive region, it may cross the x-axis at another point, but without any further info, it appears to exist primarily at the origin for graphical representations.

3. **Y-intercept \( C \) of \( f(x) \)**:
Since the function is \( f(x) = -2x \), the y-intercept occurs at \( x = 0 \):
\[
C: (0, f(0)) = (0, 0)
\]

4. **Y-intercept \( D \) of \( g(x) \)**:
To find \( D \):
\[
g(0) = 2(0) + 10 = 10 \implies D = (0, 10)
\]

### Summary of Coordinates:
- \( A = (0, 0) \)
- \( B = (0, 0) \) - As we derived, unless otherwise provided from a graphical intersection point.
- \( C = (0, 0) \)
- \( D = (0, 10) \)

### 6.2 Determine the length of \( AB \).
The length of \( AB \):
- Assuming both \( A \) and \( B \) are at the origin, hence \( AB = 0 \) (unless proven that \( B \) is elsewhere).

### 6.3 Determine the equation of the axis of symmetry of \( f(x) \).
For a linear function, the line \( f(x) = -2x \) does not have a typical axis of symmetry as it's not a parabola. Thus, it can be said:
- **No axis of symmetry** in terms; thus not applicable (optionally could present y = mx + c contextually).

### 6.4 Determine the length of \( GH \) (length between turning points or hypothesized points).
- \( f(x) \) is linear hence does not have turning points like parabolas. Here it would be flat.

### 6.5 Hence write down the values of \( x \) for which \( f(x) > 0 \).
To find where \( f(x) > 0 \):
\[
-2x > 0 \implies x < 0
\]
Thus the values of \( x \) are:
- **Any \( x < 0 \)**.

### 6.6 Determine the coordinates of \( E \), one of the points of intersection of \( f(x) \) and \( g(x) \).
To find the intersection:
Set \( f(x) = g(x) \):
\[
-2x = 2x + 10
\]
Solving:
\[
-4x = 10 \implies x = -\frac{5}{2}
\]
Substituting back to find the \( y \):
\[
f(-\frac{5}{2}) = -2 \times -\frac{5}{2} = 5
\]
So, point \( E \):
- \( E = \left(-\frac{5}{2}, 5\right) \)

### 6.7 Determine the length of \( OK \).
This question is incomplete without context to the graph or explicit lengths of designated geometry. Assuming \( OK \) corresponds to how \( O \) (the origin) relates to another point \( K \) which is diagonal or horizontal/vertical is essential for determining relative length against \( J \) and \( L \).

### Conclusion:
Clarifying graphical references pivotally adds understanding for distances between defined \( x \) and intercept outcomes of predefined geometry. The answers above stem directly from the mathematical evaluation of provided equations depending solely on spatial geometry without a figure. Please adjust as details or clarifications arise in your original query for graphical representation corrections or assumptions made therein.