Question

Find the slope of the line n perpendicular to line h and through point P. Type your answer as a fraction in lowest terms.

Answer 1

Explanation:

let the point be (h,k)

for a given line, ax+by+c

d=∣∣∣ah+bk+ca2+b2−−−−−−√∣∣∣

so, 2≤d1p+d2p≤4

2≤∣∣∣h−k2–√∣∣∣+∣∣∣h+k2–√∣∣∣≤4

22–√≤|h−k|+|h+k|

ifh>k

22–√≤h−k+h+k≤42–√

2–√≤h≤22–√

ifh<k

22–√≤−h+k+h+k≤42–√

2–√≤k≤22–√

area of shaded region

area = (22–√)2−2–√2

=6unit2