if two opposite vertices of an rectangle are - 1, 3 and 4, 0 find the coordinates of the other two vertices.
Answers
Answer:
y² - 3y + x² - 3x + 4 = 0
other vertices will lies on this circle
Step-by-step explanation:
two opposite vertices of an rectangle are - 1, 3 and 4, 0
Let say Vertex of another corner = (x , y)
(x , y) with (-1 , 3) & ( 4 , 0) will be perpendicular to each other as it is a rectangle
=> ( y - 3)/(x + 1) * (y - 0)/(x - 4) = -1
=> y² - 3y = (x + 1)(4 - x)
=> y² - 3y = -x² + 3x + 4
=> y² - 3y + x² - 3x + 4 = 0
or
Also ( 4 - (-1))² + (0 -(3)² = (y - 3)² + (x - (-1))² + (y - 0)² + (x - 4)²
=>34 = y² + 9 - 6y + x² + 1 + 2x + y² + x² + 16 - 8x
=> 2y² - 6y + 2x² -6x + 8 = 0
=> y² - 3y + x² - 3x + 4 = 0
y² - 3y + x² - 3x + 4 = 0
other vertices will lies on this circle
Answer:
B(4,3) and D(-1,0)
Step-by-step explanation:
Given:-
Two opposite vertices A(-1, 3), and C(4, 0) of the rectangle
To find:-
coordinates of other vertices
Solution:-
Let the rectangle be ABCD. We have to find B(x, y) and D(a, b)
From the graph, if we draw ⊥ from A it intersects at point D(-1, 0).
∴ Coordinates of D = (-1 , 0)
Now,
Midpoint of AC = Midpoint of BD
(4-1)÷2 = (x-1)÷2
x=4
similarly,
(3-0)÷2 = (0+y)÷2
y=3
∴ Coordinates of B are (4, 3)
