Question

A line L passes through the points (1,1) and (0,2) and another line M which is perpendicular to L passes through the point$(0,-\frac{1}{2})$ the area of the triangle formed by this lines with y-axis is

• A. $\frac{25}{16}$
• B. $\frac{25}{4}$
• C. $\frac{25}{32}$
• D. $\frac{25}{8}$

Answer 1

The correct option is A $\frac{25}{16}$

Slope of $L=\frac{2-1}{0-1}=-1$

Line L

equation of line $L$

$y-1=-1(x-1)$

$x+y=2$........(1)

Line M

equation of line $M$

$y+\frac{1}{2}=1(x-0)$

$y+\frac{1}{2}=x$.......(2)

solving (1) and (2), we get,

$y=\frac{3}{4},x=\frac{5}{4}$

$C(\frac{5}{4},\frac{3}{4})$

area of triangle

$=\frac{1}{2}\times b\times h$

$=\frac{1}{2}\times (2+\frac{1}{2})\times \frac{5}{4}$

$=\frac{1}{2}\times \frac{5}{2}\times \frac{5}{4}$

$=\frac{25}{16}$