In an equilateral triangle PQR, PA is the altitude. O is the orthocentre and PO=12 the find the value of PA.

A) \$20\$

B) \$14\$

C) \$18\$

D) \$16\$

Find the equation of a straight line parallel to the line joining the points (7,5) and (1,3) and passing through the point (–3,4).

A) \$x - 3y + 15 = 0\$

B) \$3x + y + 15 = 0)\$

C) \$x + y - 15 = 0\$

D) \$3x + 3y + 15 = 0\$

Find the equation of the straight line passing through the point \$(3,2)\$ and perpendicular to the straight line joining the points \$(4,5)\$ and \$(1,2)\$.

A) \$x + y + 6 = 0 \$

B) \$x + y - 5 = 0 \$

C) \$x + y - 6 = 0 \$

D) \$x - y + 12 = 0 \$

AD is a median of △ABC and O is the centroid such that AO = 10cm. Length of OD is,

A) \$5\$

B) \$7\$

C) \$4\$

D) \$2\$

If A(5,−1),B(−3,−2) and C(−1,8) are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.

A) centroid \$ = (\frac{1}{3}, \frac{5}{3})\$ and median \$= \sqrt{65} \$

B) centroid \$ = (\frac{2}{3}, \frac{7}{3})\$ and median \$= \sqrt{85} \$

C) centroid \$ = (\frac{1}{4}, \frac{5}83)\$ and median \$= \sqrt{55} \$

D) centroid \$ = (\frac{4}{3}, \frac{5}{8})\$ and median \$= \sqrt{75} \$