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In the diagram, points L, N, and P lie on the same line.



The diagram shows triangles L M N and N O P. The coordinates of point L are (4, 4).

Question
Triangle L M N has a vertical height of 2 units and a horizontal length of 3 units. Triangle N O P has a vertical height of 4 units and an unknown horizontal length.



Drag numbers to the lines to show the coordinates of point P.

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Coordinates of point P equals left-parenthesis
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Answer options with 20 options.

1 answer

To find the coordinates of point P given the information about triangles L M N and N O P, let's analyze the information step by step.

  1. Triangle L M N:

    • The vertical height is 2 units and the horizontal length is 3 units.
    • Assume L is at (4, 4) and since the vertical height goes "down" (typically in geometry unless specified otherwise), M would be 2 units below L (due to the vertical height).
    • Therefore, point M would be at (4, 4 - 2) = (4, 2).

    To find point N, since it is on the same line as L and P, we can infer that it lies on the same horizontal level as L because the horizontal length of 3 units goes along the x-axis. We assume point N is directly to the right of L, leading us to deduce that:

    • Point N will then be at (4 + 3, 4) = (7, 4).

  2. Triangle N O P:

    • The vertical height is 4 units.
    • This means that point O will be below point N in line with the height:

    Since N is at (7, 4), point O, going down by 4 units, would be at (7, 4 - 4) = (7, 0).

    To find point P, it also lies on the same line as L, N, and O, so we consider where it could be horizontally.

  3. Determining coordinates of Point P:

    • We do not have a defined height for triangle N O P that allows movement along the y-axis since that is already defined by vertical height.
    • Generally, the horizontal length will match from the right of N for P, thus if triangle N O P has the same horizontal stretch (assuming a typical triangle formation), we could place point P as far right or left, depending on orientation.

    Without specific instructions, the most straightforward assumption is to keep it simple. If we're assuming a similar setup horizontally along the x-axis (and with N as a reference), we could position Point P at the end of a horizontal stretch of O.

Taking these deductions, the horizontal length to P might mirror that of N to O leading to 3 additional spaces; however, without further elaboration, a sensible coordinate for P considering all factors may be assumed as:

If N = (7, 4), and assume equal length as L - then point P may coordinate at: (7, 0), thus it's ending on at least for the minimum stretch of width.

Therefore, the assumed coordinates of point P could reasonably be:

Coordinates of point P = (7, 0)

If horizontal randomly to fit constraints layout.