Math, asked by soumendas1611, 11 hours ago

Draw the graph of x + y = 4 and use it to find the area of the triangle formed by the line and coordinate axes.

Answers

Answered by mathdude500
4

\large\underline{\sf{Solution-}}

Given equation of line is

\red{\rm :\longmapsto\:x + y = 4}

Substituting 'x = 0' in the given equation, we get

\rm :\longmapsto\:0 + y = 4

\bf\implies \:y = 4

Substituting 'x = 2' in the given equation, we get

\rm :\longmapsto\:2 + y = 4

\rm :\longmapsto\:y = 4 - 2

\bf\implies \:y = 2

Substituting 'x = 4' in the given equation, we get

\rm :\longmapsto\:4 + y = 4

\rm :\longmapsto\:y = 4 - 4

\bf\implies \:y = 0

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

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

➢ Now draw a graph using the points (0 , 4), (2 , 2) & (4 , 0)

➢ See the attachment graph.

From graph, we concluded that

Required Triangle is OAB formed by the given line with coordinates axis.

Coordinates of A = (4, 0)

Coordinates of B = (0, 4)

Coordinates of C = (0, 4)

So,

Required area of triangle ABC = 1/2 × 4 × 4 = 8 square units.

Attachments:
Similar questions