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.
- France: grade 10
- Syria: grade 10
- Palestine: grade 9
- Ukraine: grade 9
- Russia: grade 9
Guide
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 = 0; to find where it meets the y-axis put x = 0.
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 = √(AO2 + BO2), the perimeter P = OA + OB + AB and the area S = OA·OB2.
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: ...".