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  • Find the ratio in which the line segment joining the points (6, 4) and (1, -7) is divided by the X- axis.

Find the ratio in which the line segment joining the points (6, 4) and (1, -7) is divided by the X- axis.

Answers (1)

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Using the Section Formula which states that if a point P(x, y) divides a line segment joining two points A(x1, y1) and B(x2, y2) in the ratio m:n, then:$$
y = \frac{m y_2 + n y_1}{m + n}
$$

here,

  • m → Part of the segment closer to point B.
  • n → Part of the segment closer to point A.
  • y → The y-coordinate of the dividing point P(x, y).

Given-

  • A(6, 4) - First endpoint of the line segment.
  • B(1, -7) - Second endpoint of the line segment.
  • The X-axis divides the line segment, meaning the y-coordinate of the dividing point is 0.

Solution- Putting all the given values in the formula,$$
0 = \frac{m(-7) + n(4)}{m+n}
$$
$$
m(-7) + n(4) = 0
$$
$$
-7m + 4n = 0
$$
$$
7m = 4n
$$
$$
\frac{m}{n} = \frac{4}{7}
$$

Therefore, the X-axis divides the line segment in the ratio 4:7.

Posted by

Saniya Khatri

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