Since the ratio of AP to PB is 1:3, we can divide the segment AB into 4 equal parts.
Let's label the points on segment AB as A(-5, y1), B(3, y2), P(x, y).
Since the x-axis ranges from -5 to 3 in increments of 1, we can divide this range into 9 equal parts (including the endpoints) to find the x-coordinate of P.
Starting from A, we count 2 parts to the right to reach P's x-coordinate. So, the x-coordinate of P is -5 + 2 = -3.
Since segment AB is divided into 4 equal parts, each part is (3 - (-5))/4 = 8/4 = 2 units long.
Starting from y1, which is the y-coordinate of A, we move 2 units up to reach the y-coordinate of P. So, the y-coordinate of P is y1 + 2.
Since we know that the ratio of AP to PB is 1:3, we can set up the following equation:
(AB - AP) / AP = PB / AP
(8 - AP) / AP = 3
Now, let's solve for AP:
8 - AP = 3AP
8 = 4AP
AP = 8/4
AP = 2
So, the length of AP is 2 units.
Since P is 2 units up from A, the y-coordinate of P is y1 + 2.
Therefore, point P is located at (-3, y1 + 2).
Segment upper A upper B is graphed on a coordinate plane. The x-axis ranges from negative 5 to 3 in increments of 1. The y-axis ranges from negative 5 to 4 in increments of 1.
Calculate point P on AB¯¯¯¯¯¯¯¯ such that the ratio of AP
to PB
is 1:3.
5 answers
sorry but your wrong
Apologies for the mistake. Let's correct the solution.
Segment AB is divided into 4 parts, with AP being one part and PB being three parts.
The total length of segment AB is 3 - (-5) = 8 units.
Since AP is one part, its length is 8/4 = 2 units.
To find the coordinates of point P, we need to determine the x-coordinate and y-coordinate separately.
The x-coordinate of A is -5, and we need to move 1 part to the right to reach P. Since each part is 8/4 = 2 units, the x-coordinate of P is -5 + 2 = -3.
Now let's determine the y-coordinate of P. The y-coordinate of A is y1, and we need to move 1 part up to reach P. Since each part is 9/4 = 2.25 units, the y-coordinate of P is y1 + 2.25.
Therefore, the coordinates of point P are (-3, y1 + 2.25).
Segment AB is divided into 4 parts, with AP being one part and PB being three parts.
The total length of segment AB is 3 - (-5) = 8 units.
Since AP is one part, its length is 8/4 = 2 units.
To find the coordinates of point P, we need to determine the x-coordinate and y-coordinate separately.
The x-coordinate of A is -5, and we need to move 1 part to the right to reach P. Since each part is 8/4 = 2 units, the x-coordinate of P is -5 + 2 = -3.
Now let's determine the y-coordinate of P. The y-coordinate of A is y1, and we need to move 1 part up to reach P. Since each part is 9/4 = 2.25 units, the y-coordinate of P is y1 + 2.25.
Therefore, the coordinates of point P are (-3, y1 + 2.25).
P(−212,−214)
upper P left parenthesis negative Start Fraction 5 over 2 End Fraction comma negative Start Fraction 9 over 2 End Fraction right parenthesis
P(−245,−235)
upper P left parenthesis negative Start Fraction 14 over 5 End Fraction comma negative Start Fraction 13 over 5 End Fraction right parenthesis
P(12,112)
upper P left parenthesis Start Fraction 1 over 2 End Fraction comma Start Fraction 3 over 2 End Fraction right parenthesis
P(−1,−1)
these are the answer choices
upper P left parenthesis negative Start Fraction 5 over 2 End Fraction comma negative Start Fraction 9 over 2 End Fraction right parenthesis
P(−245,−235)
upper P left parenthesis negative Start Fraction 14 over 5 End Fraction comma negative Start Fraction 13 over 5 End Fraction right parenthesis
P(12,112)
upper P left parenthesis Start Fraction 1 over 2 End Fraction comma Start Fraction 3 over 2 End Fraction right parenthesis
P(−1,−1)
these are the answer choices
The correct answer is P(-212, -214).