Question

what is the distance between the following points? graph of coordinate plane with two points choose 1 answer: a 5 b 7 c √12 d √28

Explanation:

Step1: Identify coordinates

First, find the coordinates of the two points. From the graph, the first point (let's say \( P \)) is at \( (4, 2) \) and the second point (let's say \( Q \)) is at \( (8, 5) \).

Step2: Apply distance formula

The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Substitute \( x_1 = 4 \), \( y_1 = 2 \), \( x_2 = 8 \), \( y_2 = 5 \):

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Wait, no, wait. Wait, \( 8 - 4 = 4 \), \( 5 - 2 = 3 \). Then \( 4^2 + 3^2 = 16 + 9 = 25 \), square root of 25 is 5? But wait, no, wait the options have \( \sqrt{28} \)? Wait, maybe I misread the coordinates. Let me check again. Wait, maybe the first point is (4, 2) and the second is (8, 5)? Wait, no, maybe the x-coordinates: 4 to 8 is 4 units, y-coordinates: 2 to 5 is 3 units. Then distance is 5? But option D is \( \sqrt{28} \). Wait, maybe I made a mistake. Wait, let's recheck the coordinates. Wait, maybe the first point is (4, 2) and the second is (8, 5)? Wait, no, maybe the y-coordinate of the second point is 5? Wait, no, maybe the first point is (4, 2) and the second is (8, 5). Wait, 8 - 4 = 4, 5 - 2 = 3. Then \( 4^2 + 3^2 = 16 + 9 = 25 \), so distance is 5? But option A is 5. Wait, but maybe I misread the coordinates. Wait, let's check again. Wait, the first point: x=4, y=2. Second point: x=8, y=5. So difference in x: 8 - 4 = 4, difference in y: 5 - 2 = 3. Then distance is \( \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \). So the answer should be A? Wait, but wait, maybe I made a mistake. Wait, maybe the coordinates are (4, 2) and (8, 5)? Wait, no, maybe the second point is (8, 5)? Wait, but let's check the options. Option A is 5, which is the result. Wait, but let's recalculate. \( (8 - 4) = 4 \), \( (5 - 2) = 3 \). \( 4^2 + 3^2 = 16 + 9 = 25 \), square root is 5. So the answer is A. But wait, maybe I misread the y-coordinate. Wait, maybe the second point is (8, 5)? Wait, the graph: the first point is at x=4, y=2 (blue dot at (4,2)), the second at x=8, y=5 (blue dot at (8,5)). So yes, distance is 5. So the correct answer is A.

Wait, but earlier I thought maybe \( \sqrt{28} \), but no, my calculation shows 5. So the answer is A.

Answer:

A. 5