Prove that the points (-5,4), (-1,-2), (5,2) lie at three of the corners of a square. Find the coordinates....

Question

Prove that the points (-5,4), (-1,-2), (5,2) lie at three of the corners of a square. Find the coordinates of the 4th corner and the area of the square

Answer 1

use the distance formula.

http://www.purplemath.com/modules/distform.htm

it's about halfway down the page, under the subheading "distance formula" in purple.

plot the points in a coordinate plane. then after you get the distance of each line, aka the length, count the same number of spaces away from the corners to complete the square. basic geometrey.

Answer 2

first you need to come to a decision the place the three corners are located then you could decide the place the fourth desires to flow you want the area from (-5,4) to (-a million,-2) (-5,4) to (5,2) and (-a million,-2) to (5,2,) 2 of those would be aspects of the sq. the third would be the diagonal of the sq. c^2=a^2+b^2 c^2=(x2-x1)^2+(y2-y1)2 the three strains c^2=(-5-(-a million))^2+(4-(-2))^2 c^2=(-5-5)^2+(4-2)^2 c^2=(-a million-5)^2+(-2-2)^2 c^2= -4^2+6^2=sixteen+36=50 c^2= -10^2+2^2=one hundred+4=104 c^2=-6^2+-4^2=36+sixteen=50 so (-5,4) to (5,2) is the diagonal and (-a million,-2) is the third nook [because of the fact the section is an element squared, we already comprehend the section is 50] we ought to discover the slope of the diagonal the slope of the perpendicular the midpoint of the diagonal the element equidistant from the third element (-a million,2) to the fourth nook for the period of the midpoint of the perpendicular slope (y2-y1)/x2-x1) (4-2)/(-5-2) -2/7 the perpendicular is 7/2 the midpoint of diagonal (x1+x2)/2,(y1+y2)/2 (-5+5)/2,(4+2)/2 (0,3) now we want the element two times the area of (-a million,-2) to (0,3) on the different element of (0,3) from (-a million,-2) x: from -a million to 0 is a million 0+a million x=a million y: from -2 to 3 is 5 3+5 8 the fourth nook is (a million,8) and the section [from above] is 50

Answer 3

Call the points A, B, C

Distances AB and BC are both sq root (4.(4+9)) = 2 sq root(13).

slopes

AB is -6/4 = -3/2
BC is 4/6 = 2/3

So the two sides are equal length and at right angles - i.e. two sides of a square.

The fourth point is (1,8). D

The sides are all sq root (4.(4+9)) = 2 sq root(13).
Area = 52