obs23 wrote:

In the xy coordinate plane, does the point (3,4) lie on line t?

(1) The line 5y-45=-x is perpendicular to the line t.

(2) The line with the equation \(y= \frac{3}{4}x - 11\) intersects the line t when y=-11.

Please show a step by step approach here and explain why it is not

. I do not understand the official explanation.

Keep in mind, there are two ways in which you can define a line t:

- You are given two distinct points that lie on that line. You join the two points and you have a defined line.

- You are given one point and the slope of the line. You make a line with the given slope on the point.

Question: In the xy coordinate plane, does the point (3,4) lie on line t?

You need to define line t to figure out if a point lies on it.

(1) The line 5y-45=-x is perpendicular to the line t.

This gives you the slope of line t but you don't have any point on it. So you cannot define line t.

Not sufficient.

(2) The line with the equation \(y= \frac{3}{4}x - 11\) intersects the line t when y=-11.

When y = -11, you can find the value of co-ordinate x by plugging in \(y= \frac{3}{4}x - 11\).

So you will have a point which lies on line t. But you don't have another point.

Hence you cannot define line t using this statement alone.

Using both stmnts, you get the slope of line t and a point that lies on it. This will help you define t uniquely. So you will be able to find out whether (3, 4) lies on it.

Sufficient.

Answer (C)

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