Math, asked by soumya1400, 4 months ago

draw the graph of equation 2x-3y=2 and x-2y=8 determine the coordinates of the vertices of the triangle formed by two lines and the y-axis and calculate the area of triangular region formed​

Answers

Answered by mathdude500
10

❥︎Question :-

  • Draw the graph of equation 2x - 3y = 2 and x - 2y = 8. Determine the coordinates of the vertices of the triangle formed by two lines and the y-axis and calculate the area of triangular region formed.

❥︎Answer

❥︎Given :-

  • Two lines 2x - 3y = 2 and x - 2y = 8.

❥︎To find :-

  • The coordinates of the vertices of the triangle formed by two lines and the y-axis
  • The area of triangular region formed.

Solution :-

❥︎Consider line (1), 2x - 3y = 2.

⟶The points lies on line (1) are

\begin{gathered}\boxed{\begin{array}{c|c|c|c|c|c}\bf x&\sf 1&\sf 4&\sf 7 &\sf\\\frac{\qquad \quad \qquad}{}&\frac{\quad \qquad \qquad}{}&\frac{\qquad \quad\qquad}{}&\frac{\qquad \quad \qquad}{}& \\\bf \ y&\sf 0&\sf 2&\sf 4&  \end{array}}\end{gathered}

❥︎Consider line (2), x - 2y = 8

⟶The points lies on line (2) are

\begin{gathered}\boxed{\begin{array}{c|c|c|c|c|c}\bf x&\sf 8&\sf 10&\sf 12 &\sf\\\frac{\qquad \quad \qquad}{}&\frac{\quad \qquad \qquad}{}&\frac{\qquad \quad\qquad}{}&\frac{\qquad \quad \qquad}{}& \\\bf \ y&\sf 0&\sf 1&\sf 2&  \end{array}}\end{gathered}

❥︎Plot these points on the graph paper,

Blue represents 2x - 3y = 2 and red represents x - 2y = 8.

⟶The required triangle is ABC bounded by the given two lines ans y - axis, having vertices

\bf \:⟶A( - 20, - 14)

\bf \:⟶B(0, - 4)

\bf \:⟶C(0, - \dfrac{2}{3} )

❥︎Now, Required area of triangle ABC

⟶ Area of triangle ADC - Area of triangle ADB

\bf \:⟶\dfrac{1}{2}  \times 20 \times \dfrac{40}{3}  - \dfrac{1}{2}  \times 20 \times 10

\bf \:⟶\dfrac{1}{2}  \times 20 \times (\dfrac{40}{3}  - 10)

\bf \:⟶10 \times \dfrac{10}{3}

\bf \:⟶\dfrac{100}{3}  \: sq. \: units

Attachments:
Similar questions