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Vedmedyk [2.9K]
3 years ago
8

Point B has coordinates ​(​1,2​). The​ x-coordinate of point A is -8. The distance between point A and point B is 15 units. What

are the possible coordinates of point​ A?
Mathematics
1 answer:
Xelga [282]3 years ago
8 0

Answer:

The possible coordinates of point A are A_{1} (x,y) = (-8, 14) and A_{2} (x,y) = (-8, -10), respectively.

Step-by-step explanation:

From Analytical Geometry, we have the Equation of the Distance of a Line Segment between two points:

l_{AB} = \sqrt{(x_{B}-x_{A})^{2} + (y_{B}-y_{A})^{2}} (1)

Where:

l_{AB} - Length of the line segment AB.

x_{A}, x_{B} - x-coordinates of points A and B.

y_{A}, y_{B} - y-coordinates of points A and B.

If we know that l_{AB} = 15, x_{A} = -8, x_{B} = 1 and y_{B} = 2, then the possible coordinates of point A is:

\sqrt{(1+8)^{2}+(2-y_{A})^{2}} = 15

81 + (2-y_{A})^{2} = 225

(2-y_{A})^{2} = 144

2-y_{A} = \pm 12

There are two possible solutions:

1) 2-y_{A} = -12

y_{A} = 14

2) 2 - y_{A} = 12

y_{A} = -10

The possible coordinates of point A are A_{1} (x,y) = (-8, 14) and A_{2} (x,y) = (-8, -10), respectively.

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If F(x) = 7x - 6, which of the following is the inverse of F(x)?
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<u>Explanation:</u>

We have to first find the mid-point of the segment, the formula for which is

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It is the point at which the segment will be bisected.

Since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula \frac{y_2-y_1}{x_2-x_1}

The slope is \frac{-5-1}{7+1} = -\frac{2}{3}

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of  -\frac{2}{3} is \frac{3}{2}

To write an equation, substitute the values in y = mx + c

WHere,

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y = \frac{3}{2} x - \frac{11}{2}

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