Question

please refer the attachment, Class 10, coordinate geometry

Answer 1

Answer:

AD=(√130)/2 units

Centroid=[-4/3,2]

Step-by-step explanation:

median always divides opposite into two equal parts

if AD is median then D(x,y) must be equidistant and colliner to B(0,4) C(-5,3)

(x,y)=$( \frac{x'+x"}{2} , \frac{y'+y"}{2} )$

     =(0-5/2, 4+3/2)

     =(-5/2,7/2)

AD=$\sqrt{(x''-x')^{2}+ (y''-y')^{2} }$

    =$\sqrt{(1+\frac{5}{2}) ^{2}+(-1-\frac{7}{2}) ^{2} }$

    =$\sqrt{(\frac{7}{2}) ^{2}+(\frac{9}{2} )^{2} }$

    =$\sqrt{\frac{49+81}{4} }$

    =$\sqrt{\frac{130}{4} }$

    =$\frac{\sqrt{130} }{2}$

Centroid=$(\frac{x'+x''+x'''}{3} , \frac{y'+y''+y'''}{3} )$

              =$(\frac{1+0-5}{3} , \frac{-1+4+3}{3} )$

              =$(\frac{-4}{3} , 2)$