Question

Find condition for the points (a,0),(h,k) and (0,b) are collinear

Answer 1

Step-by-step explanation:

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Answer 2

The condition for the points (a,0), (h,k) and (0,b) to be collinear is $ka+bh-ba=0.$

• Points that are on the same straight line are referred to as collinear points. They must lie on the same straight line, even if they don't have to be co-planar. The Latin terms "col" and "linear," where "col" means "together" and "linear" means "in the same line," are the source of the English word "colinear." Collinearity is the state of being shared by two points.
• Collinearity is the quality of two points being parallel to one another. Any three or more points are only considered to be collinear if they are situated along the same straight line. There is only one line that can pass through three locations that are collinear.

Here, according to the given information, the points are given as,

(a,0), (h,k) and (0,b).

Now, in order to make the points collinear, the slope of the line joining the first two points must be same as that of the slop of the line joining the next two points.

Slope of the line joining the (a,0) and (h,k) = $\frac{k-0}{h-a} .$

Slope of the line joining the (h,k) and (0,b) = $\frac{b-k}{0-h}$

Now, equating, we get,

$\frac{k}{h-a} =\frac{k-b}{h}$

Or, $kh = kh-ka-bh+ba$

Or, $ka+bh-ba=0.$

Hence, the condition for the points (a,0), (h,k) and (0,b) to be collinear is $ka+bh-ba=0.$

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