KCET · Maths · Straight Lines
The points \(A(1,2), B(2,4)\) and \(C(4,8)\) form a/an
- A isosceles triangle
- B equilateral triangle
- C straight line
- D right angled triangle
Answer & Solution
Correct Answer
(C) straight line
Step-by-step Solution
Detailed explanation
Given points, \(A(1,2), B(2,4), C(4,8)\)
\(A B=\sqrt{(2-1)^{2}+(4-2)^{2}}=\sqrt{1+4}=\sqrt{5}\)
\(B C=\sqrt{(4-2)^{2}+(8-4)^{2}}=\sqrt{4+16}=\sqrt{20}\)
\(C A=\sqrt{(1-4)^{2}+(2-8)^{2}}=\sqrt{9+36}=\sqrt{45}\)
Slope of \(A B=\frac{4-2}{2-1}=2\)
Slope of \(B C=\frac{8-4}{4-2}=2\)
Slope of \(C A=\frac{2-8}{1-4}=2\)
So, the three points form a straight line or three points are collinear.
\(A B=\sqrt{(2-1)^{2}+(4-2)^{2}}=\sqrt{1+4}=\sqrt{5}\)
\(B C=\sqrt{(4-2)^{2}+(8-4)^{2}}=\sqrt{4+16}=\sqrt{20}\)
\(C A=\sqrt{(1-4)^{2}+(2-8)^{2}}=\sqrt{9+36}=\sqrt{45}\)
Slope of \(A B=\frac{4-2}{2-1}=2\)
Slope of \(B C=\frac{8-4}{4-2}=2\)
Slope of \(C A=\frac{2-8}{1-4}=2\)
So, the three points form a straight line or three points are collinear.
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