A(0, 2) and C(4, 0) are opposite vertices of the square ABCD.
What is the equation of the straight line through B and D?
- Ay = −2x + 5
- By = −12x − 3
- Cy = −12x + 2
- Dy = x
- Ey = 2x − 3
- Fy = 2x + 2
Show the answer and worked solution
answer · E
- Ay = −2x + 5
- By = −12x − 3
- Cy = −12x + 2
- Dy = x
- Ey = 2x − 3
- Fy = 2x + 2
There is no need to find B and D themselves. In a square the two diagonals bisect each other at right angles, so BD passes through the midpoint of AC, which is (2, 1), and is perpendicular to AC. The gradient of AC is 0−24−0 = −12, so BD has gradient 2. Through (2, 1) that gives y − 1 = 2(x−2), i.e. y = 2x − 3.