﻿ In the figure, given coordinates of point A is (3,4) in the rectangular coordinates. Let

#### Multiple Choice Question (MCQ)

In the figure, given coordinates of point A is (3,4) in the rectangular coordinates. Let point P is a dynamic point on the positive x axis such that \triangle AOP is an isosceles triangle. How many such triangle could be formed?

1. ×

1

2. ×

2

3. 3

4. ×

4

Collected in the board: Coordinate geometry

Steven Zheng posted 5 months ago

1. Moving the point P along the x axis finds 3 isosceles triangles could be formed.

Since point A is a fixed point, using the distance formula between two points gives

AO = \sqrt{3^3+4^2}

\cos \angle AOP = \dfrac{3}{5}

1. When AP = OP

OP = \dfrac{OD}{\cos \angle AOP}

= \dfrac{\dfrac{AO}{2} }{\cos \angle AOP}

= \dfrac{2.5}{\dfrac{3}{5} } = \dfrac{5}{2}\cdot \dfrac{5}{3}=\dfrac{25}{6}

The coodinates of P is (\dfrac{25}{6} ,0)

2. When OP = OA = 5

The coodinates of P is (5,0)

3. When OP = AP

The coodinates of P is (6,0)

Steven Zheng posted 5 months ago

Scroll to Top