Question

pq and rs are shown on the coordinate plane below. draw exactly one point that meets the following conditions. • the point drawn is coplanar with points p, q, r, and s. • the point drawn is collinear with p and q.

Explanation:

Step1: Identify line PQ

First, we look at the coordinates of points P and Q. From the graph, we can see the line PQ (the blue line with a negative slope). We need to find a point that is collinear with P and Q (so on line PQ) and coplanar with P, Q, R, S (which they all are since they are on the same coordinate plane).

Step2: Find collinear point on PQ

We can extend the line PQ (or find a point already on the line segment or its extension) that is also on the same plane as R, S (which is the coordinate plane, so all these points are coplanar). Looking at the line PQ, we can see that we can pick a point on the line PQ. For example, we can find the equation of line PQ or just visually identify a point on PQ. Let's assume we look at the line PQ: from the graph, the line PQ passes through certain grid points. We can pick a point on PQ, say, by extending or using the existing line. The key is that the point must be on line PQ (collinear with P and Q) and on the same plane (which is the coordinate plane, so all points here are coplanar). So we can draw a point on the line PQ (the line connecting P and Q). For example, if we look at the line PQ, we can find a point like (let's check coordinates) - but visually, the line PQ is the one with points P (around (3,4) maybe? Wait, looking at the graph, P is at (3,4) maybe? Wait, the grid: let's see, the x-axis and y-axis. Wait, the line RS is the one with positive slope, passing through R (left bottom), S (middle), and P? Wait, no, P is on both? Wait, no, PQ and RS intersect at P? Wait, the problem says PQ and RS are shown. Wait, maybe P is the intersection point? Wait, the point we need is collinear with P and Q (so on line PQ) and coplanar with P, Q, R, S (which they all are). So we just need to pick a point on line PQ. Let's say, for example, the point can be any point on the line segment PQ or its extension. So we can draw a point on line PQ.

Answer:

To solve this, we identify the line \( \overleftrightarrow{PQ} \) (the line containing points \( P \) and \( Q \)). Any point on this line (e.g., a point along the line segment \( PQ \) or its extension) will be collinear with \( P \) and \( Q \) and coplanar with \( P, Q, R, S \) (since all points lie on the coordinate plane). For example, we can draw a point on \( \overleftrightarrow{PQ} \) (e.g., by extending the line or using a point on the segment). Visually, on the given graph, we can mark a point on the line connecting \( P \) and \( Q \).