Question

URGENT
please reply quick and right​

Answer 1

Answer:

a.

b. y-coordinate, x-coordinate

c. 3x-5y-7=0

3(2k-1)-5(k)-7=0

6k-3-5k-7=0

k-10=0

k=10

d. Let the rectangle be OABC with the vertex O at the origin.

Let OA be the longer side.

∴ The co-ordinate of O is O(0,0).

Since one of the vertex is in the third quadrant and the longer side of length 5 units lie on the x-axis, the co-ordinate of A is A(−5,0).

Also, the rectangle lie in the III quadrant.

∴ The side OC will lie on the y-axis to the negative direction.

Then, the length of OC is 3 units.

∴ The co-ordinates of C will be C(0,−3).

Then obviously, the co-ordinates of B will be (−5,−3).

Here, OC∥AB and ∠AOC=90

o

, hence is a rectangle.

Therefore, the vertices of the rectangle are O(0,0),A(−5,0),B(−5,−3),C(0,−3).