Without using Pythagoras theorem, show that the points A(0, 4), B… - Vidyadip

Question

Without using Pythagoras theorem, show that the points A(0, 4), B(1, 2) and C(3, 3) are the vertices of a right angled triangle.

✓

Answer

Slope of $\text{AB}=\frac{2-4}{1-0}=-2$ Slope of $\text{BC}=\frac{3-2}{3-1}=\frac{1}{2}$ slope of AB × slope of BC $=-2\times\frac{1}{2}=-1$ $\therefore$ Anlgle between AB and BC $=\frac{\pi}{2}$ $\therefore$ ABC are the vertices of a right angled triangle.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from The Straight Lines→The Straight Lines — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find: $\text{A}\cap\text{D}$

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$

Find the general solutions of the following equations: $\cos\text{x}=-\frac{\sqrt3}{2}$

If the straight line through the point P (3, 4) makes an angle $\frac{\pi}{6}$ with the x-axis and meets the line 12x + 5y + 10 = 0 at Q, find the length PQ.

How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?

For some constants a and b, find the derivative of (x - a)(x - b)

A box contains 1 red, one 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Which trem of the A.P. 3, 8, 13, ...os 248?

Find: $\lim\limits_{\text{x}\rightarrow2}[\text{x}]$

Find the slope of a line, which passes through the origin and mid-point of the line segment joining the points P(0, - 4) and B(8, 0).