Question

Find the coordinates of the points on y axis which are at a distance of 15 units from the point (9,12)

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Answer 1

The coordinates of the points on the y-axis that are at a distance of 15 units from the point (9, 12) are (0, 0) and (0, 24).

Explanation:

Any point on the y-axis has an x-value of zero. Therefore, (0, y).

To find the distance between any two points, we can use the distance formula.

`\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=√((x_2-x_1)^2+(y_2-y_1)^2)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}`

Given the distance between point (9, 12) and point (0, y) is 15 units:

• (x₁, y₁) = (9, 12)
• (x₂, y₂) = (0, y)
• d = 15

Substitute these values into the distance formula and solve for y:

`\begin{aligned}√((0-9)^2 + (y-12)^2) &= 15 \\√(81+ (y-12)^2)&=15 \\81+(y-12)^2&=225\\(y-12)^2&=144\\√((y-12)^2)&=√(144)\\y-12&=\pm12\\y&=12\pm12\\y&=0, 24\end{aligned}`

Therefore, the coordinates of the points on the y-axis that are at a distance of 15 units from the point (9, 12) are:

• (0, 0) and (0, 24)