Concept 7.4
Where an Axis Cuts a Segment
Source: NCERT Mathematics, Class 1010 minute lesson
Formal statement
A point on the x-axis has y-coordinate 0, and a point on the y-axis has x-coordinate 0. To find the ratio in which an axis divides a segment, take the ratio as k : 1 and set the matching coordinate of the section formula to 0.
The intuition
NCERT asks: in what ratio does the y-axis divide the segment joining (5, −6) and (−1, −4)? The crossing point is on the y-axis, so its x-coordinate is 0.
With ratio k : 1, x = (−k + 5)/(k + 1) = 0 gives k = 5. The ratio is 5 : 1, and the point is (0, −13/3).
The attention
Look at which coordinate the axis makes zero.
On the y-axis: x = 0, so (5 − k)/(k + 1) = 0; not y = 0
Look hereNot here
- Look here
- The coordinate that is 0 on that axis. Every point on the y-axis has x = 0. That one fact turns the section formula into an equation for k.
- Not here
- The other coordinate. It's tempting to set y = 0 because the question says 'y-axis'. But y = 0 is the x-axis.
- What it teaches
- Translate a picture into one equation before reaching for a formula.