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?
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.
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)
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]
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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