answer: (-8,4) are the coordinates of a
step-by-step explanation:
let the side of square abcd is x .
thus the area of square abcd is
.
now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x
( because ad is the side of square)
and, according to the question,
the areas of square abcd and right ead are equal.
⇒![x^2=1/2\times ea\times ad](/tex.php?f=x^2=1/2\times ea\times ad)
⇒ea=2x
thus, ea: ab=2: 1
therefore, point a divides line segment eb into the ratio 2: 1.
⇒ by sectional formula coordinates of a are,
=![(\frac{2\times -7+1\times -10}{2+1},\frac{2\times 2+1\times 8}{2+1})](/tex.php?f=(\frac{2\times -7+1\times -10}{2+1},\frac{2\times 2+1\times 8}{2+1}))
= ![(\frac{-24}{3}, \frac{12}{3})](/tex.php?f=(\frac{-24}{3}, \frac{12}{3}))
=(-8, 4)
thus the coordinates of a are (-8,4)