Maths-
General
Easy

Question

The points open parentheses 0 comma 8 over 3 close parentheses comma left parenthesis 1 comma 3 right parenthesis and (82, 30) are vertices of

  1. an obtuse – angled Δ
  2. an acute – angled Δ
  3. a right – angled Δ
  4. none of these

The correct answer is: none of these


    Here we have given 3 vertices.
    A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
    m = change in y/change in x = Δy/Δx
    where “m” is the slope of a line.
    The slope of the line can also be represented by
    tan θ = Δy/Δx
    Slope, m = Change in y-coordinates/Change in x-coordinates
    m = (y2 – y1)/(x2 – x1)
    Here we will use the same formula to find the slope. If slope matches, then its not a triangle.
    L e t space A left parenthesis x 1 comma y 1 right parenthesis space equals space left parenthesis 0 comma space 8 divided by 3 right parenthesis comma space B left parenthesis x 2 comma y 2 right parenthesis space equals space left parenthesis 1 comma 3 right parenthesis comma space C left parenthesis x 3 comma y 3 right parenthesis space equals space left parenthesis 82 comma 30 right parenthesis.
S l o p e space o f space A B space i s colon space fraction numerator 3 space minus space left parenthesis begin display style 8 over 3 end style right parenthesis space over denominator 1 minus 0 end fraction
S l o p e space o f space A B space i s colon 1 third
S l o p e space o f space B C space i s colon space fraction numerator 30 minus 3 over denominator 82 minus 1 end fraction
S l o p e space o f space B C space i s colon space 1 third
S o space t h e space s l o p e s space a r e space s a m e.
T h e n space A comma space B space a n d space C a r e space c o l l i n e a r space a n d space w i l l space n o t space f o r m space t r i a n g l e.

    Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure. A straight line is an endless one-dimensional figure that has no width. Here we have given the points as (0, 8/3), (1, 3) and (82, 30), we have to find these are the vertices of which figure.

    Here we used the concept of slope and slope of a line where we found the slope of the line of side off triangle and found that the slopes of th e lines are same and hence A, B and C were collinear. So it cannot form any triangle and its a straight line on which all the three points are lying.

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