Question

Of the following four points, three are an equal distance from the point $A(0,1)$ and the line $y=-1 .$ (a) Identify which three, and (b) find any two additional points that satisfy these conditions. $B(-6,9) \quad C(4,4) \quad D(-2 \sqrt{2}, 6) \quad E(4 \sqrt{2}, 8)$.

Name: Problem 23, Chapter 9: Precalculus
Uploaded: 2020-12-19T11:18:38-08:00
Duration: 5 min 46 s
Channel: Harmender Singh Yadav
Description: Of the following four points, three are an equal distance from the point A(0,1) and the line y=-1 . (a) Identify which three, and (b) find any two additional points that satisfy these conditions. B(-6,9) C(4,4) D(-2 √(2), 6) E(4 √(2), 8).

   Of the following four points, three are an equal distance from the point $A(0,1)$ and the line $y=-1 .$ (a) Identify which three, and (b) find any two additional points that satisfy these conditions. $B(-6,9) \quad C(4,4) \quad D(-2 \sqrt{2}, 6) \quad E(4 \sqrt{2}, 8)$.

Precalculus

John W. Coburn 2nd Edition

Chapter 9, Problem 23

Instant Answer

Solved by Expert Harmender Singh Yadav

12/19/2020

Step 1

We can use the distance formula which is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. For point B, the distance is $\sqrt{(-6-0)^2 + (9-1)^2} = \sqrt{36 + 64} = \sqrt{100} = 10$. For point C, the distance is $\sqrt{(4-0)^2 + (4-1)^2} = \sqrt{16 + 9} = \sqrt{25} = Show more…

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Of the following four points, three are an equal distance from the point $A(0,1)$ and the line $y=-1 .$ (a) Identify which three, and (b) find any two additional points that satisfy these conditions. $B(-6,9) \quad C(4,4) \quad D(-2 \sqrt{2}, 6) \quad E(4 \sqrt{2}, 8)$.

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Key Concepts

Distance Formula

The distance formula is used to determine the distance between any two points in the Cartesian plane. It is derived from the Pythagorean theorem and is essential for calculating the straight-line distance between two points given their coordinates.

Point-to-Line Distance Formula

This formula calculates the perpendicular distance from a point to a given line in the plane. It provides the shortest distance between the point and the line and is crucial for problems involving distances from a point to a fixed line.

Parabola (Focus-Directrix Definition)

A parabola is the set of all points that are equidistant from a fixed point, called the focus, and a fixed line, known as the directrix. This focus-directrix property is central to understanding the geometric nature of parabolas and solving problems where distances from a point and a line are equal.

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