In the rectangular coordinate system above the area of PQR is what fraction of the area of LMN
From the attached figure we find the area of PQR and area of LMN
WE know the formula for area of triangle = [tex] \frac{1}{2} [/tex] * base * height
In the triangle PQR,
Base PR= 4
Height = distance between x- axis and point Q = 4
Area of the triangle PQR = [tex] \frac{1}{2} [/tex] * 4 * 4 = 8
Similarly we find the area of LMN
In the triangle LMN,
Base LN= 12
Height = distance between x- axis and point M = 12
Area of the triangle LMN = [tex] \frac{1}{2} [/tex] * 12 * 12 = 72
Hence , [tex] \frac{area PQR}{Area LMN} [/tex] = [tex] \frac{8}{72} = \frac{1}{9} [/tex]
Area of PQR = [tex] \frac{1}{9} [/tex] of the area of LMN
