The first line passes through points (0; 45) and (3; 6). The second line passes through points (1; 2)

| June 20, 2021 | education

The first line passes through points (0; 45) and (3; 6). The second line passes through points (1; 2) and (-4; 7). Find the coordinates of the common point of these two lines.

Points A (0; 4.5), B (3; 6), C (1; 2) and D (-4; 7) are given. The first line passes through points A and B, and the second line passes through points C and D. You need to determine the coordinates of the intersection of these two lines.
We use the formula (x – x1) / (x2 – x1) = (y – y1) / (y2 – y1) of the equation of the straight line passing through two points M1 (x1; y1) and M2 (x2; y2). We have: for the straight line AB: (x – 0) / (3 – 0) = (y – 4.5) / (6 – 4.5) or y = x / 2 + 4.5; similarly, for the straight line CD: (x – 1) / (-4 – 1) = (y – 2) / (7 – 2) or y = -x + 3.
The point of intersection of lines AB and CD will be denoted by K. In order to find the desired coordinates of the point K, we solve the jointly found equations: y = x / 2 + 4.5 and y = -x + 3. We have: x / 2 + 4, 5 = -x + 3 or 1.5 * x = -1.5, whence x = -1.5 / 1.5 = -1. Then y = – (- 1) + 3 = 1 + 3 = 4. So, point K has coordinates (-1; 4).
Answer: (-1; 4).



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