Chapter 2

Coordinate Geometry and the Circle (Pure 1)

Straight lines from coordinates, the circle in both of its forms, and the tangent property that reduces most circle questions to line questions you can already do.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Measurement and Geometry)ตรงกับ ม.4 เรขาคณิตวิเคราะห์ (เพิ่มเติม) ทั้งเส้นตรงและวงกลม
Common Core (US): G-GPE, G-C
Cambridge: 9709 Pure Mathematics 1 — Coordinate geometry

2.1 Lines, gradients and distances

The standard results

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} m_{1} m_{2} = - 1 for perpendicular lines

ตัวอย่าง

The line through $A (1, 3)$ and $B (7, 5)$ is one side of a square. Find the equation of the line through $B$ perpendicular to $A B$ .

วิธีทำ

1.Gradient of $A B$ : $\frac{5 - 3}{7 - 1} = \frac{1}{3}$
2.Perpendicular gradient: $- 3$
3.Through $B (7, 5)$ : $y - 5 = - 3 (x - 7)$

ตอบ $y = - 3 x + 26$

เคล็ดลับ

Sketch the points before doing anything, even roughly. Coordinate geometry questions are almost always about a shape, and a sketch turns "find the fourth vertex" from an algebra problem into something you can nearly read off.

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