The two lines y=x and x=-4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x axis?

Ans:

excellent explanation by Bunuel.

these type of questions are easily solved using Graph or drawing lines on co-ordinate axis.

even if you dont know how to draw a graph.

here is solution.

given

y=x and x =-4 intersect.

so, point of intersection between y=x and x =-4 will be (-4,-4)

we have to find the area covered by lines y=x,x=-4 & y=0 (i.e x-axis)

so,

and point of intersection between x=-4 and y=0 will be (-4,0)

so we have a triangle with following axis.(0,0), (-4,0) & (-4,-4)

here, if you can draw a picture of how this line will look in co-ordinate axis, you will find a right angle triangle whose altitude is 4 and base is 4.

so, area will be =1/2 x 4 x 4 = 8 (ans)

if you don't have any idea about how to draw a line or place some points on co-ordinate axis.

remember some old school day formula,

you can calculate the area of triangle by following formula:

1. first calculate the distance between three points by formula ;

Distance (a,b,c) = Sqrt[(x1-x2)^2+(y1-y2)^2]

here, a=4,b=4,c=4sqrt(2)

2. then

calculate s= (a+b+c)/2

and area of triangle is = Sqrt [(s-a)^2+(s-b)^2+(s-c)^2]

after calculation area of triangle will come as 8.

I hope my explanation will be clear.

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