Question

What is the distance of the point (3,-4) from x-axis. What is the sum of the abscissa of any three points on the y axis.

Answer 1

Hint:Distance between two coordinates (a, b) and (c, d) is given by Euclidean distance formula which is given by, $\sqrt {{{(c - a)}^2} + {{(d - b)}^2}} $ . Here we need to apply this formula replacing (a, b) with (3, -4) and (c, d) with (3, 0) as they have given the x-axis as the other point where its y coordinate becomes zero for all points in the x-axis. And they have asked to find the sum of the abscissa of points on y axis. Abscissa refers to the horizontal axis (x-axis).

Complete step-by-step answer:
Euclidean distance formula is given by, $\sqrt {{{(c - a)}^2} + {{(d - b)}^2}} $ for points (a, b) and (c, d). Here we replace those points with (3, -4) and x axis points. Here, considering the perpendicular distance from the point (3, -4) to the x axis, we choose x axis point (3, 0). Thus the distance between them will be,
Distance, d$ = $ $\sqrt {{{(3 - 3)}^2} + {{(0 - ( - 4))}^2}} $
$ = \sqrt {{0^2} + {{16}^2}} $
$ = 16$
Abscissa refers to the horizontal axis or x-axis. Thus in case of y axis, x-coordinate will always be zero. Thus the abscissa of any point on y axis will be zero. They have asked for the sum of abscissa of any three points on y axis. Let those points be (0, a), (0, b), (0, c). Sum of abscissa will be the sum of x-coordinates of all three points which is zero.

Distance of the point (3, -4 from x axis) = 16
Sum of abscissa of any three points on y-axis =0

Note:Abscissa and ordinate are the terms concerned with a point on XY plane. Abscissa refers to the horizontal axis or x-axis, and ordinate represents the vertical length or y-axis. Thus for a point (a, b), the first coordinate refers to the abscissa and the second coordinate refers to the ordinate.Students should remember the distance between two points (a, b) and (c, d) i.e $\sqrt {{{(c - a)}^2} + {{(d - b)}^2}} $ for solving these types of questions.