Question

Use the image to answer the question. Find the coordinates of point X on segment AB¯¯¯¯¯¯¯¯ that partitions the segment into the ratio AX:BX = 1:2 . (1 point) Responses X(−413,−10) upper X left parenthesis negative Start Fraction 13 over 3 End Fraction comma negative 10 right parenthesis X(−423,213) upper X left parenthesis negative Start Fraction 19 over 3 End Fraction comma Start Fraction 11 over 3 End Fraction right parenthesis X(−1013,5) upper X left parenthesis negative Start Fraction 31 over 3 End Fraction comma 5 right parenthesis X(−313,83) upper X left parenthesis negative Start Fraction 10 over 3 End Fraction comma Start Fraction 8 over 3 End Fraction right parenthesis Skip to navigation

Answer 1

To find the coordinates of point \( X \) that divides segment \( AB \) in the ratio \( AX:BX = 1:2 \), we can use the section formula.

Let the coordinates of point \( A \) be \( (x_1, y_1) \) and those of point \( B \) be \( (x_2, y_2) \). The coordinates of the dividing point \( X \) can be calculated as:

\[ X = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

where \( m = 2 \) and \( n = 1 \) (since \( AX:BX = 1:2 \)), which means:

\[ X = \left( \frac{2x_2 + 1x_1}{2 + 1}, \frac{2y_2 + 1y_1}{2 + 1} \right) = \left( \frac{2x_2 + x_1}{3}, \frac{2y_2 + y_1}{3} \right) \]

If the coordinates of point \( A \) and \( B \) are given in the image (which you mentioned but cannot provide here), please input the coordinates for \( A \) and \( B \), and I will calculate the coordinates for \( X \).

Let me know the specific coordinates for points \( A \) and \( B \), and I will help you find \( X \).

Answer 2

B is located at (-8, 5) and A is at (-3, 1).

Answer 3

Given the coordinates of points \( A(-3, 1) \) and \( B(-8, 5) \), we need to find the coordinates of point \( X \) that divides the segment \( AB \) in the ratio \( AX:BX = 1:2 \).

Using the section formula, where \( m = 2 \) and \( n = 1 \):

\[ X = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

Substituting in the values:

• \( x_1 = -3 \)
• \( y_1 = 1 \)
• \( x_2 = -8 \)
• \( y_2 = 5 \)
• \( m = 2 \)
• \( n = 1 \)

Now let's calculate:

\[ X_x = \frac{2(-8) + 1(-3)}{2 + 1} = \frac{-16 - 3}{3} = \frac{-19}{3} \]

\[ X_y = \frac{2(5) + 1(1)}{2 + 1} = \frac{10 + 1}{3} = \frac{11}{3} \]

Thus, the coordinates of point \( X \) are:

\[ X\left(-\frac{19}{3}, \frac{11}{3}\right) \]

Now, we can compare the result with the provided options. The correct coordinates of point \( X \) from your list are:

\( X\left(-\frac{19}{3}, \frac{11}{3}\right) \).

Answer 4

The answers are,
X(−413,−10) upper X left parenthesis negative Start Fraction 13 over 3 End Fraction comma negative 10 right parenthesis X(−423,213) upper X left parenthesis negative Start Fraction 19 over 3 End Fraction comma Start Fraction 11 over 3 End Fraction right parenthesis X(−1013,5) upper X left parenthesis negative Start Fraction 31 over 3 End Fraction comma 5 right parenthesis X(−313,83) upper X left parenthesis negative Start Fraction 10 over 3 End Fraction comma Start Fraction 8 over 3 End Fraction right parenthesis

Answer 5

Thank you for providing the answer options. Given the calculated coordinates of point \( X \) earlier, which are:

\[ X\left(-\frac{19}{3}, \frac{11}{3}\right) \]

Let's express this in decimal form to match with the options:

1. \(-\frac{19}{3} \approx -6.33\)
2. \(\frac{11}{3} \approx 3.67\)

Now, let's find which option corresponds to those coordinates.

Among the options you provided, the correct form associated with the calculated coordinates would be:

• \(X\left(-\frac{19}{3}, \frac{11}{3}\right)\)

This matches with:

• X(−423,213), which should be \(X\left(-\frac{19}{3}, \frac{11}{3}\right)\).

To clarify:

• \(X(-423, 213)\) is \(X\left(-\frac{19}{3}, \frac{11}{3}\right)\).

Thus, the correct choice from the options given is:

\(X\left(-\frac{19}{3}, \frac{11}{3}\right)\).

Answer 6

there is no X(-19/3, 11/3).

Answer 7

I apologize for the misunderstanding. Let's go through the options again closely based on the calculations we made for the coordinates of point \( X \) that divides segment \( AB \) in the ratio \( AX:BX = 1:2 \).

We calculated:

\[ X\left(-\frac{19}{3}, \frac{11}{3}\right) \]

Now let's compare this more carefully with the provided answers:

1. X(−413,−10)
2. X\(\left(-\frac{13}{3}, -10\right)\)
3. X(−423,213)
4. X\(\left(-\frac{19}{3}, \frac{11}{3}\right)\)
5. X(−1013,5)
6. X\(\left(-\frac{31}{3}, 5\right)\)
7. X(−313,83)
8. X\(\left(-\frac{10}{3}, \frac{8}{3}\right)\)

From our calculation:

• The x-coordinate \( -\frac{19}{3} \) does not appear exactly as is among the provided options. But let's convert it to a decimal:

  • \( -\frac{19}{3} \) equals approximately \( -6.33 \).

• The y-coordinate \( \frac{11}{3} \) equals approximately \( 3.67 \).

Based on the options available, it appears that none of them directly states \( X\left(-\frac{19}{3}, \frac{11}{3}\right) \).

However, to check we can see if option X\(\left(-\frac{19}{3}, \frac{11}{3}\right)\) corresponds or is formatted incorrectly in your input.

Looking closely at the available option again indicates:

• X\(\left(-\frac{19}{3}, \frac{11}{3}\right)\) is present in the form of X(−423,213), likely for a specific selection interpretation for the answer options.

I apologize for the oversight in mentioning earlier. It seems you were correct; it’s consistent with the computed values yet rephrased or aligned per selections.

Thank you for your patience, and if there's anything specific about this selection you need, please let me know!