Question

The plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$ meets the coordinate axes at A, B, C respectively. D and E are the mid-points of AB and AC respectively. Coordinates of the mid-point of DE are

• A. $(a,\frac{b}{4},\frac{c}{4})$
• B. $(\frac{a}{4},b,\frac{c}{4})$
• C. $(\frac{a}{4},\frac{b}{4},c)$
• D. $(\frac{a}{2},\frac{b}{4},\frac{c}{4})$.

Answer 1

The correct option is D $(\frac{a}{2},\frac{b}{4},\frac{c}{4})$.

$A(a,0,0),B(0,b,0),C(0,0,c),D(\frac{a}{2},\frac{b}{2},0),E(\frac{a}{2},0,\frac{c}{2})$
So midpoint of DE is $(\frac{a}{2},\frac{b}{4},\frac{c}{4})$.