KnowledgeBoat Logo
|

Mathematics

Assertion (A): Point (0, 9) is a point on y-axis which is equidistant from points (6, 5) and (-4, 3).

Reason (R): Abscissa of a point on y-axis is 0.

  1. Assertion (A) is true, Reason (R) is false.

  2. Assertion (A) is false, Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Coordinate Geometry

1 Like

Answer

A point lies on the y-axis if and only if its x-coordinate (abscissa) is 0.

∴ Reason (R) is true.

Let P = (0, 9), A = (6, 5), and B = (-4, 3).

By formula,

Distance between two points = (x2−x1)2+(y2−y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

PA=(6−0)2+(5−9)2=62+(−4)2=36+16=52.PB=(−4−0)2+(3−9)2=(−4)2+(−6)2=16+36=52PA = \sqrt{(6 - 0)^2 + (5 - 9)^2}\\[1em] = \sqrt{6^2 + (-4)^2}\\[1em] = \sqrt{36 + 16}\\[1em] = \sqrt{52}. \\[1em] PB = \sqrt{(-4 - 0)^2 + (3 - 9)^2}\\[1em] = \sqrt{(-4)^2 + (-6)^2}\\[1em] = \sqrt{16 + 36}\\[1em] = \sqrt{52}

Since PA = PB = 52\sqrt{52}.

​Therefore, the point (0, 9) is a point on y-axis which is equidistant from (6, 5) and (-4, 3).

∴ Assertion (A) is true.

∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is not the correct reason (or explanation) for Assertion (A).

Hence, option 4 is the correct option.

Answered By

1 Like

Related Questions