A line and the axes: triangle, perimeter and area
Find where a line ax + by = c meets the axes, the perimeter and area of the triangle it cuts off, and where two lines meet.
- سوريا: الصف ١٠
- فلسطين: الصف ٩
- أوكرانيا: الصف ٩
- روسيا: الصف ٩
- فرنسا: الصف ١٠
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الدليل
In Ukrainian Grade 9 geometry (section 3, topic 10) a line is given by ax + by = c. To find where it meets the x-axis put y = ٠; to find where it meets the y-axis put x = ٠.
A line that meets both axes forms a right triangle AOB with them, O being the origin. Its legs are the absolute values of the coordinates of A and B, the hypotenuse is AB = √(AO٢ + BO٢), the perimeter P = OA + OB + AB and the area S = OA·OB٢.
The meeting point of two lines is on both lines, so its coordinates solve the system of their equations. Write the solution as the textbook does: "Solution. ... Answer: ...".